@Artobe
Let’s do it step by step.
We first have to make sure that the updater tool is able to read (to get access to) the SPIROM, for that we might also need to try other (newer or older) updater tools.
Once we gain access to the SPIROM we can look for the best firmware for your controller.
Please read my post #365 (and maybe #287 too), this will tell you that not always the latest/newest firmware is the best choice for your controller/system.
But first, let’s try the MS-DOS usb drive and run your current updater tool from that.
@Artobe
I’m sorry. You’ve done extra work.
Basically follow the instructions of Meadow.
Please try this too.
But it is older than the current version
The probability of success is low.
Please try it on Windows to make a trial.
This is the last of what I can do.
Please do not give up even if you fail.
Asus USB 3.0 FW Update Tool v1.0.zip (311 KB)
Has anyone managed to successfully update the firmware of the card below?
https://www.delock.com/produkte/G_89299/merkmale.html
This is a combo card with two external USB 3.0 and two internal SATA III ports.
I was not able to find sufficient information to attempt to update either the USB or the SATA firmware.
@kyriacos
May I ask for what specific reason(s) you would like to update the firmware of your card?
I mean, when the card works properly (according specs) and without errors or any failures it might be best to not touch, change or update the firmware at all (never change a running system).
@Meadow
The card is not detected by the motherboard bios and as a result any drive connected to the SATA ports is not bootable. No message appears from the card at boot and I think that the USB ports could perform faster.
The Specification is telling me:
• Asmedia chipset
• 2 x external USB 3.0 type A
• 2 x internal SATA 6 Gb/s
• Data transfer rate:
USB 3.0 up to 5 Gb/s
SATA up to 6 Gb/s
PCI Express x4 up to 1000 MB/s
• PCI Express x4
• Supports PCI Express 2.0
• Not bootable
• Hot Swap
There is a bullet named: "Not bootable".
Doesn’t this mean you can’t boot from the card at all (not from SATA and not from USB)?
Looks to me as if the card works like specified, but I can be wrong.
@Meadow
I have conflicting information about the "Not bootable" statement and I know that the card uses an old firmware. I am willing to give it a try if anyone else managed to successfully update the card.
@kyriacos
To update the USB 3.0 firmware on your card, did you already try the updater tools (for DOS / for Windows) found in this thread to see/check whether or not they can be used for your card (use the read commands only in order not to change the firmware on your card by accident)?
When using the DOS updater tool I would recommend to run the updater tool twice, once with the card installed and once without the card installed and check if there is a difference in the output logging. If there is no difference then the DOS updater tool can’t access/read the USB SPIROM (if your card has any, that is).
@Meadow
I have not tried anything yet, because I read about an unsuccessful attempt to update the SATA firmware in the Firmware for Asmedia Sata 6G Controllers topic. I was hoping that someone else with the same card might had better luck with updating the USB firmware.
@Meadow
Rufus can’t create MSDOS bootable USB-drives as it’s missing a .dll for that.
Edit: Luckily I had a Win7-install around, however with the MSDOS instead of FreeDOS I get the same error SPIROM not found (-8) with all updaters.
@nobi 
@Artobe
Please try the updater tool from attached old FW package (if you haven’t got this FW package already).
Do not use u.bat nor C:\104xfwdl /U
Use only
C:\104xfwdl /d
and
C:\104xfwdl /A
to test
Asmedia ASM-104x USB 3.0 Firmware Version 110315_01_02_30 - FW0315.zip (195 KB)
@Artobe
Seemingly /A is not implemented in the old version of the updater tool. Personally I used a newer version of the updater tool together with the old .bin of the old FW package which I still use today, a version which works rock solid for me.
Give /C and /T first a try with the old version of updater tool, then try /U too with a newer .bin and then with the .bin of this old FW packagce. Note that the latter may be older than the one you have (as is reported by /d).
No change, I’m ready to give up trying 
@Artobe
It seems that no updater tool (whether DOS or Windows) is able to access the SPIROM on your motherboard.
I have looked around on the internet regarding the issue you have and found the following two threads which may be of interest to you (if you not already found them yourself that is).
1) https://www.overclockers.com/forums/show…4-USB-3-problem
2) https://forums.tomshardware.com/threads/…-issues.382274/
In thread 1) user richard.tyfty seems to have fixed the same kind of issue by updating the motherboard BIOS to version: “P1.70 BIOS 06/06/12” (see post #1 and #16)
In thread 2) post #11 someone is using BIOS version 1.40 with working Asmedia USB3 ports (He tried 1.70 briefly but went back to 1.40)
What BIOS version do you use at the moment?
Did you already try above mentioned BIOS versions?
@Artobe
In addition to the BIOS questions:
May I know something more about the current status and history of your Asmedia USB3 ports?
1) Apart from not being able to update the USB3 firmware: Do the Asmedia USB3 ports currently work (normally) within Windows (i.e. can you read from and write to a usb stick)?
2) Did the Asmedia USB3 ports ever work "normally" in Windows (at full or lower speed or intermittently)?
3) Is the current Asmedia USB3 firmware the original firmware that came installed with the motherboard?
4) Did you ever (try to) update the Asmedia USB3 firmware before? When so did you encounter an error while updating the USB3 firmware leaving you with the update issue you have now?
I’m using 3.0 modded to include NVME support from MDCLAB.
1)They work fine except my fastest USB3 stick doesn’t and I hoped it would fix that.
2)Always did work normally, other slower USB3 sticks work fine also.
3)I’d guess so.
4)A lot of times but never managed it to change version I suppose as the errors in Windows and DOS cropped up, just as they do now.
It might be the case that the modded (non standard) BIOS 3.0 doesn’t work well in combination with the Asmedia updater tools (which might be developed/writtten for older BIOS versions).
It would be worth the try to flash BIOS 1.40 or 1.70 and test if you can get the updater tools to work (in DOS mode) then revert back to 3.0, but I’m not sure if that is possible to do for your setup.
I’d rather not - downgrading a BIOS is one of those few cases that has an increased chance to brick it and already pushed my luck by not bricking my Asmedia USB controller courtesy to all those flashing attempts ;).
Don’t have a BIOS programmer and 2nd PC set up atm either.
Anyway, thanks for the tips @Meadow and @nobi , really appreciate trying to get it to work but alas it shouldn’t be :D.