I'm with lane00. Liquid Plumber has worked more effectively than Drano for me on clearing bathroom drains. For shower drains, I've found that the main culprit is usually hair!
We've put on a screen under our main drain that helps prevent hairs from falling through. Once we've put that in, we've found that our shower drain has not backed up in a while.
What you may want to do to get started off with a 'clean slate' is have a plumber use their snake device to really clear out your drain. (I know its a cost but think of it as an investment in the future!). Once that's done, try adding some other item like the screen or one of those 'drain-catcher' devices to help prevent hair from falling through. That way, your use of Liquid Plumber should be way less frequent.
After several failures with commercial clog removal, I went with a more natural approach that was recommended on This Old House. Put a couple tablespoons of baking soda into the clogged drain, and follow up with a little bit of vinegar. The two will react to each other, and will start fizzing. This fizzing action can clear up minor clogs. Follow up with some boiling water to remove any leftover clog residue, and you're all set.
Also, sometimes when you pour the unclogging chemicals down the drain, they're able to dissolve it enough, but you need to create a vacuum to help the clog pass down the drain. Try using a plunger a few times over the drain, and re-check to see if water passes. It really works!