Some strings hold up better and can be reused with more success than others. Most steel strings can go on and off of basses repeatedly without a lot of problems. I have a 4 year old set of Superflexibles that's been through the mill and they still sound fine. The silk at the peg end is kind of a mess at this point.
Synthetics like Obligato don't fare as well. It seems that these type of strings lose their life more quickly and taking down the tension and bringing it back up repeatedly only accelerates the process.
Plain gut stings are fairly durable. Flatwound gut like Olive and Eudoxa seem prone to developing separations in the windings the more you take them off and put them back on. Roundwound gut are more durable. They can start to lose their life and the windings may come loose though.