The supplement is called "betaine hydrochloride" or "HCL betaine". I don't take it much because I don't like to rely on a pill, but I do take it sometimes when I eat meat.
There are lots of factors in whether we produce enough stomach acids or not -- a bunch of them which I already mentioned. It definitely seems to vary... it's not like you either DO or DON'T produce enough stomach acids all the time. Know what I mean? You have to follow rules for good digestion. (There's lot of info about this on http://www.askshelley.com, in the FAQ.)
I just read recently that stress makes us more acidic/unable to produce adequate stomach acids. So don't eat when stressed/upset! I don't know if that's a factor for you or not.
Meat is acid-forming, so when you eat it, it's especially important to get extra minerals/vitamins afterward, to balance that out and make you more alkaline again.