I've bought the same model Regal Reso about six months ago and so far I've not had any problems with it staying in tune. I've changed strings about four times since then but have not gotten up the nerve to remove all of them at once for fear of moving the biscuit, meanwhile the fretboard continues to collect skin cells and oil....Maybe it's just that the biscuit have moved a bit, wouldn't take much to wack it out. My vote's to spend an afternoon fooling around with different settings, unless the neck/body joint shows signs of the bolts loosening.
Good luck Grab, hope it ain't nothin' serious. The Regal seems like a well made guitar to me. It's not a National but I can still make the mortgage payment for what this Korean Kuzzin' costs.