First if you are talking about total proteins you may run an SDS Page and do coomassie blue staining. If your proteins are ok you will see different bands along the gel. if they are degraded the bands are not sharp.
Second if you have a purified protein you do the same SDS PAGE and do a silver staining if the amount of your protein is very low. if not the coomassie blue will let you know if your protein is degraded or not.
If you do Western blot and your protein is degraded you will see nothing at all
To better answer your question, it would be Nice to have more détail about your samples like Heydies is asking. Also ars your samples purified proteins or relatively raw cellular extracts? Do you have antibody against your protein? How were your samples prepared and conserved?
Many proteins are very sensitive toward different factors , such as pH, temperature and different enzymatic activity in your sample (proteases). These can easily be detected as previous comments mentioned with SDS-PAGE. All proteins can be degraded through 2 different pathways: Protease-pathway or Proteasome-pathway. Adding protease inhibitors mix will prevent protein degradation via protease-pathway. By adding proteasome-inhibitors (such as MG115, MG132) will inhibit the degradation via proteasome (ubiqiutylation). If you want to study the half-life of your protein then you need to run Puls-Chase experiment and label your proteins/cells with e.g. radioactive aa such as S35 (met/Cys) then by adding cold Met/Cys to the cells and taking out cells during different time and continue with lyses the cells and run Ip (immunoprecipitation). You can find more information in one of my articles :