I got a Forster trimmer off the EE a while back, and got it setup for .223, trimming to 1.75. I trimmed quite a few cases, and then the next time I went to trim, I checked, and it was trimming about 1.745. I adjusted it, and now I am finding that it will go out of adjustment after 15 or so cases. It has gone as far as 1.735. I am also finding that some of the chamfering is way off, and some of the ends of my cases are trimming unevenly. At the moment, I don't have it mounted, I just hold it in place, and trim. I wouldn't think this would matter as everything should be adjusted and holding firm. My question is, do these trimmers suck in general, did I just get a bad one, or does having it mounted and permanently attached actually matter despite all adjustments being made?

I've used my Forster for 40 years with no complaints other than my own neglect.  Any tool needs to be checked and rechecked for tightness.  The Forster especially so, since the set screws that hold adjustment tighten into hardened steel.  If the set screws don't hold, make sure your shaft isn't greased where they tighten...got to be squeaky clean there.

Also, DO fasten the tool down.....at least screw it to a 2x4 and clamp the 2x4 to the bench.  Operator technique is important.....for one thing don't keep forcing the shaft into the brass....trim until it smooths out and the chips quit flying and no more.

Since you mentioned chamfering I get it that you are using the 3-way trimmer over the built-in trimmer.  Now you have another setscrew to make sure is clean and tight.  It slides over the top of the shaft and cutter.  Slide it all the way in until it stops and tighten.  Do check tightness often.....on any tool.

Should work fine then.  If not call Forster....you may have a rare dud.

I see Dryflash3 posted with another valid thought while I was typing.  Concerning that....it is important to check your brass heads for nicks and damage that would effect how it sits in the collet....and it is your responsibility to make sure, as he said, to make sure the base is flat in the bottom of the collet.  That's not hard, but you can speed up and dumb-proof the tool...(that'd be me)...by mounting it vertically.  That's not necessary if you take the time to make sure it's lined up in the hole when the pilot goes in the neck and you press the cutter firmly against the mouth before you tighten the collet or start turning the handle..

The video below shows what I did to mine after 38 years or so of using it by hand.  Buying a new progressive makes you impatient...
http://s935.photobucket.com/user/gstrad/media/ForsterImproved-1.mp4.html

Also I think the heads are screwed to the base, make sure the screws are tight.

My guess is if you mount it on a piece of wood it will work correctly.  

I've used my Forster for many years with no issues.