Thats a cool guitar! I've never played an Eastwood but would really like to.
It's a bolt-on neck right? So really even if it does pull back and push forward easily it should be returning to the same position. Usually if it's a neck problem all the strings go sharp or flat the same amount.
The first things I would check before worrying too much about the neck:
strings binding in nut - sometimes the string grooves in the nut are not cut wide enough and the strings will bind there causing tuning issues. Solution to that is adding lubricant to the groove (simple as pencil lead) or getting a nut file to enlarge them. Google 'strings binding in nut' for way more info.tuners not stable - sometimes bad (or cheap) tuning pegs don't hold the string at the proper tension. Meaning they give way a little bit when bending strings causing overall tuning of the strings to go flat. Maybe your bus' vibrations are causing the tuners to move a bit.
These are just a few things to check out. There is lots more involved when it comes to stabilizing your tuning. Let us know what you find out.
