It's hard to come up with an idea of what this might be.
The only thing I can think of from what you describe is that the valve that diverts the hot water from the boiler to the cylinder is either opening less and less over time, or is gradually furring up over time. This may lead to the behaviour you are seeing.
Basically there are two two way or one three way valve(s) on a heating system.
These valves divert water in the heating circuit either into the hot water cylinder to heat up the hot water, into the radiator circuit to heat up the radiators or both circuits simultaneously.
If the value that controls the water flow into the hot water cylinder opens less and less over time, then the flow would gradually reduce and the amount of energy going into the hot water cylinder would reduce. This would mean there was not enough flow to re heat the water while you were showering.
http://gasboilerforums.com/wiringdiagrams.html
This shows the two system types, a Y type and an S Type.
The Y type has one 3 port value (hence the Y) and the S type two two port values.
Sometimes you can actually see the valves switch, they are normally quite close to the cylinder itself.
I don't know if this is what is happening with your system, but is a potential explanation. The valves do tend to fail on a fairly regular basis as they are moving parts. You can often get replacement heads (motors) for the valves.
Someone had an issue with a valve failure on here a couple of month ago. Can't remember who.