Yes it does!

It all depends on the protein stability, some like Lysozyme and Ubiquitin can undergo several freezing cycles, others just can't. This has to do with the so called cold denaturation. Hydration of proteins changes in freezing condition and can affect the 3D fold, sometime in an irreversible way. If your protein is particularly unstable you might think of using cryo-protectant.  

Thanks!

the chance of pregnancy is nearly the same with frozen cycles nowadays. but it may affect the protein status of the cells

https://bitesizebio.com/19700/freeze-thaw-cycles-and-why-we-shouldnt-do-it/

Freeze-thaw—you know it’s bad for your samples, don’t you? While working in the lab, you have most likely heard someone say ‘aliquot your protein/cells/DNA/RNA to avoid too many freeze-thaw cycles.’ But do you actually understand why?

You probably thought that avoiding freeze-thaw cycles had something to do with damaging cell structure as well as proteins or DNA/RNA—and you would be right.