Now I'm confused...is it that the suction cups won't hold? Or that the pump won't stay in the stand?
If it's the latter, it's like @BlackSheepOG said, the pumps have a sweet spot in the holder. The holder really only holds it from moving L or R. Forward & Back (at least all my pumps) is not a lot of pressure. So, if it's too far forward or backward, it won't hold it L or R either.
If it's like all the other pumps I've seen, a hose or a connection must be pushing it out of the sweet spot. Because if it's in the holder, it should stay. It sounds like a hose (maybe it's cold & inflexible) is moving it around on you.