I have one of those guitars. Mine happens to stay in tune well, but I think components on the "lesser" guitars are a little more hit and miss.

If this is the only set of strings you've had on this guitar, then you might want to try another set, just to be sure. The occasional set of bum strings is made by any company.

Otherwise, you are probably right on the mark. I have a cheap guitar to keep in the workshop with sucky tuners and the damn thing never stays in tune. (Not that it would anyway in that environment.)

Grover's a good brand. Also Schaller and Gotoh. Check out Stewart Macdonald http://www.stewmac.com/shop/Tuners/Guitar,_solid_peghead_tuners.html