Good luck. I don't think that the problem is the CPS, but it would not hurt to have a new one as they can crap out on you at the worst of times.
Let us know if you find a solution to the problem.
Calypso Red 1992 525i with 183K miles
1991 735i - Sold
1992 525i - Sold
1995 325is - Sold
2000 528i - Sold