If you're an undergrad and are getting rejected from these programs I wouldn't take it too hard at all tbh. You have options. Depending on what your profile looks like currently:
- in your undergrad did you take mathsey courses? Real analysis? Maybe even some grad level micro or something. If yes, then masters will will add less to your profile than a predoc/RA
- did you RA for a professor and is that professor willing to give you a strong letter? If yes then doing another RA ship/predoc may not be that useful.
So I would say balance these two objectives out. In the end either won't be a bad choice but masters programs may be expensive.