1) Create More Friction
The caps on tension rods are often made of plastic, but even rubber ones are so incompressible that moist, smooth surfaces such as tile or fiberglass can't hold them. You can fix that by gluing rubber shelf lining material to the ends with strong glue - two-part epoxy or contact cement. The lining material won't damage the wall and is easy to trim to the contours of the caps with scissors. Tightening the tension rod enough to compress the liner should make the rod secure enough to hold even a heavy shower curtain...Hmm, wonder if it would bunch up if it moves?
2) Secure The Ends
If the walls on either side of the shower are drywall, you may not be able to tighten the tension rod enough without cracking the walls. Closet pole holders will keep the rod from falling. Each one needs only a single screw sunk into a plastic wall anchor. If you don't like the store-bought pole holders, make your own from any kind of wood. Any shape will do, as long as you drill recesses wide enough for the rod. Paint them the wall color to hide them, or spruce them up with another color and make them a feature...Not very subtle but would work if it's going into drywall.
3) Secure The Middle
This duct tape idea comes from 2.thriftyfun.com, By Katie
Take it down and screw it out until it is longer than the space between the two walls. Then you'll have to really PRESS it back up but it should hold.
If the problem is that your rod screws itself back in and gets too small that way...I'd say if some duct tape on it doesn't keep in from screwing itself in, pitch it and get a new one...Talk about not being subtle - duct tape?
Conclusion: There is No Good Solution For Tension Rods Falling So Stop Trying...Here's The Answer...
4) No-Drill Adapter + Rotator Rod
Solve your tension rod problem and get the latest in bathroom function and decor!
The patented No-Drill Adapters made exclusively for the Rotator Rod - the only curved shower rod that ROTATES IN AND OUT, assure secure installation onto tile or fiberglass without drilling holes. ABSOLUTELY NO FALLING! They're also safe for apartments because you can remove them with a little elbow grease and some Acetone. The fact that the Rotator Rod can be secured without drilling is only one of the many benefits it offers.