Play detected with the forearm off grasping the gun by the bbls is indicative of the gun being off face. Continued shooting will only loosen it further. If it is a quality gun, best to get it tightened up now while it is easily asccomplished. If a hardware store gun then it kinda becomes a personal call. You will probably pay a smith a minimum of one six bits to tighten a double up and put it back on face correctly. That's minimum, you can easily spend more.
Also, in the FWIW area, I know of and have seen guns with slight play that don't see much shooting use each season, but get carried about in the field as if they did. A box or two of appropriate cartridges per annum does not seem to have worsened matters much, if at all. I suspect, but cannot prove that many older SxS's with a bit of looseness got that way from 'magnumitis', i.e., shooting cartridges wholey unsuited to the guns intended use.
Some inexpensive guns were just that and they developed play quickly because of improper hardening, poor fit or both. Repairing one of those is generally not satisfactory.
