this product was the first cordless set-up i bought after buying pc from new. it performed the same tricks that you are experiencing, and most of the time "failed to grab" on the mat.
eventually so fed up with it, and yes keyboard was fine, i sacked it.
i was fortunaye enough to spot acordless optical set-up in "computer world" for only £25. and whilst it heavy on batteries and the key board is a little "gritty" the mouse performs superbly.
beware battery drain though as when they are low, the mouse takes on a mind of it's own .
as for the old one...gave it a mate and he's had no problems...must be us...
all the best