Personally not experiencing this.
I too have never seen this problem (in the forums or personally) in relation to avast, which I have been using for over 11 years and on XP Pro SP3 OS for some considerable time (unintended pun). During all this time I have not seen any difference/inconsistency/change in the system time.
My system clock is off by a few seconds slow over a week or so, this inaccuracy has been consistent and I use a little tool (About Time) to connect and correct this. Though if I remember rightly there may well be a setting in the OS to connect with an atomic clock to keep it in sync.
There is a possibility that you may need to change the motherboard battery, that can effect the time, but I would have though it more slowing it than speeding it up (or getting the date/month/year completely wrong also).
Avast has no requirement (much less the functionality) to adjust the system clock.