[Frank Richards]

Like En Sabah Nerd, I too have had activity and motion throughout the house cause vibrations that caused my figures to fall as well. No matter how stiff or loose a figure's joints are, it's just an inevitability . Well, from my experience anyways.

It took me a while to get past the often unsightly look of little plastic stands keeping my figures vertical, but after constantly having to reset displays of Marvel Legends that tumbled like dominos, I started buying those packs of figures stands from shops like Entertainment Earth.

Also, although I currently only have a couple, those figure stands from Bandai are amazing. They're sturdy, adjustable, and are especially great for flying and/or hovering characters. Imagine those old Toy Biz Marvel Legends stands, only 1000X better.
They can get pricey, but Amazon frequently has them for reasonable prices.

Another option, besides stands, is that blue poster mounting putty. The higher quality brands, from my experience, don't leave any sort of residue. In my opinion, this isn't an ideal option, but it can be a temporary solution until you find something better. It sure beats risky falls and time-consuming resets.