From what I've read on power supplies, the should be no more than a ±5% tolerance, so you're looking at something like 11.4v-12.6v as acceptable. Anything outside of that range will either over or under power whatever you're connected to leading to undesired results.
If your power supply is only putting out 10.44v, there's likely something wrong with it (old?) and anything relying on 12v may not work properly. How are the other voltages? They should be 5 and 3.3, with the same general ±5%.
Power supplies are not user serviceable. If it's not working properly, you're best off replacing it.
