Can you survive with recurrent cancer after chemo and mastectomy?

It is posswible.: If the cancer only came back locally and there is no evidence of spread, say on a pet scan, then survival after local surgery, chemotherapy (and possibly radiation) is possible.

Yes, it is possible: Despites chemotherapy and mastectomy etc- breast cancer, sometimes, can still come back. The risk for recurrent will depend on the stage, biology of the cancer, treatment received etc. When it comes back- then more treatment would be needed. If that comes back locally- it can still be cured, but, if that comes back as a metastatic disease- eventhough it is treatable-it is incurable unfortunately.