I tried with a new battery, still the same. I have not use the cheapy DMM for more than a year. Used it last week to measure my Li-ion cells and it was behaving oddly. In the end, had to borrow my brother's DMM to measure instead.
The Vichy VC99 is a great DMM. One of my best buys in the electronics area.
You can see my impressions of it and other similar multimeters (pre buy) here: https://budgetlightforum.com/t/-/1555 and its capability of measuring frequency here: https://budgetlightforum.com/t/-/1844 . It really is great for flashlight hobbyists (just buy a better pair of test leads for larger than 1.5A measurements) and also very useful around the house (don't forget to change the fuses to ceramic, for much better protection).
I don't know about reading drift since I don't have a precise power supply, but the VC99 readings are very close to two el-cheapo VC921 I have (very very good multimeters if you don't need current or temperature, extremely good continuity test and very fast autoranging) and even the two 3$ and 7$ crappymeters I have (for over a year now) give the same results, and as the saying goes - six Chinese DMMs can't be all wrong... I wouldn't worry too much about this issue, especially if you're not into precise electronics (in this case just buy a Fluke ;) ).
Dave Jones from the EEVBlog reviewed the VC99 http://www.youtube.com/watch?v=ZoeUgMFLyAw (summary here: http://www.eevblog.com/files/EEVblog_50_Dollar_Multimeter_Shootout.pdf ) and found it lacking, but I think he expects too much of a cheap multimeter, and his comparison was unfair at times.
I don't have that Vichi, but AFAIK they are very good. But if you need something more compact, try UTI-T UT33 series DMMs (I really like my UT33A, you can find it for about 18 bucks)
Hei SashiX, did you mean UNI-T UT33A? What do you think of it? I've just ordered one as "backup" DMM from here. With standard cable is able to read +3A?