Don't you have a plastic C-clip that goes around the center tube to keep the reel from riding up?
All of my plastic tanks have them. When I use a single reel, either 120 or 35, it needs to be on there or else the reel has a tendency to ride up. The only time I don't need it is when I have two reels (in a two-reel tank) which fill the entire vertical space.
Sometimes, if those clips get old, they don't hold tight enough. They either crack or lose their elasticity and, thus, can't grip the center tube.
If you have clips and you used one, check it to be sure it holds. If you don't have clips, look for some. If you can't find any, I like Ian's idea.
In fact, I just might do that instead of using clips. I imagine that might work better.