Solutions for the AMS having issues feeding filament (feeding back and forth multiple times and asking for a retry after multiple failures)...
1 Internal bowden issues
If your internal bowden clamp (the push down to release ring black clip device that holds your bowden in place to the extruder) is frayed then this can cause the AMS to feed filament back and forth and promote constant retry events on the touch screen UI.
This bowden also pokes just outside the rear of the printer.
In this scenario, please replace that bowden tube with a suitable length of spare bowden (Bambu supply plenty of spare tubing but you can pick up more if required on Amazon cheaply).
2 External bowden issues
If your bowden on the rear of the AMS keeps popping out of it's slot and feeding filament like mad, requiring you to stop a print and unload and basically panic, you probably need a replacement part.
If your Bambu X1C is within the 1st year of guarantee you should be able to obtain this part free from Bambu. This is the part you need: https://uk.store.bambulab.com/collections/accessories-for-x1-series/products/ams-internal-hub-unit
There is a guide to installation here: https://wiki.bambulab.com/en/x1/maintenance/replace-filament-hub
3 Bowden feeding to the AMS hub kinked
If the bowden on the rear of the AMS that feeds into the AMS hub on the rear of the printer is kinked, perhaps due to poor printer orientation c.f. the AMS position, then that will prevent the filament from feeding in to the AMS hub.
If this happens, you may be able to get away with simply reorienting the printer so the bowden is no longer kinked. Worst case scenario, replace the bowden that enters the rear of the AMS and feeds into the AMS hub on the rear of the printer.
4 The extruder and/or hotend may be clogged.
In this case, I recommend cleaning one or both of those while they are hot to ensure that there is no filament blocking the feeding path for printing.
Personally, I can recommend a noclogger tool (the short variant) from noclogger.com that can be used on this printer and others to carefully clean out the two pieces of hardware down to the nozzle while the hotend is hot, after removing the bowden tube and front plastic housing on the toolhead.
Once this has been done, reinsert the bowden securely and replace the front toolhead housing (be careful not to remove the connector to the toolhead front plastic piece housing while doing all of this but it is easy to reinsert it if this happens), then resume your print.
5 Your filament is going back and forth repeatedly and it won't go into the extruder.
It's possible your cutting blade is blunt; consider replacing it.
6 Last resort
Refer to BambuAMSCleaning.md. This is quite a lot more work but is likely to resolve your issues.
CAVEAT
These are all the issues I've come across to date; feel free to refer to the official Bambu wiki. There may well be others that cause the AMS to flash red or simply feed the filament back and forth multiple times then fail to continue printing.
I plan on maintaining this little document (and others) for the use of the community.