Well there are 2 X 12V supplies. Each can usually supply 7A of current. The 12V main is shared with circuits on the board that also require 12V and those circuits consume between 0.5 and 1A leaving about 6A for users. While its not on the data-sheet these supplies can surge up to 10A easily, but tend to get rather hot when doing so.
The supplies are excellent and very robust (you can put a metal object across the output of the power supplies the supply will shut down gracefully and come back right afterwards without any issues) however they do have limitations. In particular they take a few hundred milliseconds to respond to large changes in load - so if you have a load where the power consumption jumps around a lot (A WiFi router is a classic example - as a packet gets transmitted the power consumption jumps) you can sometimes have problems and the capacitor is there to smooth out those problems.
If the capacitor has become detached AND you have a load that jumps around you are likely to have a problem. You can reattach the capacitor, or simply try switching to the from Aux to main or main to aux as the case may be.