SRP with random, but constant private-value b
If you use a $g^b$ value between sessions, you allow an attacker to test multiple passwords for the second session; this invalidates the security goal for SRP.

Here is how the attack looks like:

For the first session, the attacker logs in using a password he does know.  The server sends the value $B = kv + g^b$; the attacker knows $k$ (that's derived from common data), he knows $v$ (that's derived from the password he knows), and so can recover $g^b$

For the second session, the attacker listens into a login that uses a password he does not know.  Again, the server sends the value $B = k'v' + g^b$ (where $k', v'$ are different values for this session), as he now knows $g^b$ (and can derive $k'$, he can recover $v'$; he can then go through his dictionary, and test the various passwords against $v'$.