When you hit the run button the second time, spectre will be re-running from what is in memory. It's possible that you have multiple operating points and your circuit is converging on a different solution after the first run.
In order to find out the spectre version - this will appear at the top of the spectre output log, and also "spectre -W" will tell you from the UNIX command line - but I'd check the log file.
You can also try setting "rebuildmatrix=yes" on the Simulator->Options->Analog form (if it's not on the form, type it in the additional parameters field). That said, if there is more than one operating point, maybe you need to investigate that. Perhaps you can check if the PSS simulation is finding the same oscillation frequency the first and second time you run it in ADE? It should tell you at the end of the PSS simulation what the final oscillation frequency is (and you can get this on the direct plot form too) - maybe it's converged on a different solution for the oscillation frequency?