I use a hot water pump for my shower (it is not a combi boiler). The pressure and temperature are excellent on taps but when I switch it to the shower it is fine for a minute and then starts getting cold. The issue is that it is too sensitive to cold water and a very small change in cold water tap makes it frozen or very hot!!! the issue is just in shower.
this sounds like a problem with a thermostatic balancing valve in the shower valve. you may have to pull the cartridge and clean it out or replace it. these valves use a setup that can act strangely with time and gunk. start with the simplest thing first.