A lot of answers that are not appropriate to the question :-)
Checkboard has given the answer in official wording. Here is a simple version:
- once you are navigating towards the failed SID Navaid (remember, the original question is about SID, not approach), you must be above MSA UNLESS IT'S A P-RNAV SID (I am assuming here we are talking about minimum B-RNAV equipped aircraft).
Simples.
So it all depends where that failed NAVAID is in the SID. On a side note, you are allowed to START a turn towards the failed Navaid below MSA (e.g. when passing 2000', turn towards ABC). You just need to be above it once your FMGS starts tracking towards it (using GPS/IRS). Again, all of this does not apply in the case of P-RNAV.
P