Thanks! That's what I have come to find out. But it was suggested that I use it anyway.
Here is the feedback I got from SAS:
The "accuracy was lost" warning means that in compiling the exact conditional distribution, some frequencies became extremely large. See "Exact Conditional Logistic Regression" in the PROC LOGISTIC documentation:
http://support.sas.com/91doc/getDoc/statug.hlp/logistic_sect42.htm
See also the comments toward the end of the "Computational Resources for Exact Conditional Logistic Regression":
http://support.sas.com/91doc/getDoc/statug.hlp/logistic_sect49.htm
As noted there, this message isn't necessarily problematic. It's just letting you know that the exact counts could not be maintained. Given the complexity of the exact algorithm, it's not really possible to track the cause of this message back to some feature in the data or model, but this problem is increasingly likely as the data set size increases. For data sets which are too large for the exact method, the Monte Carlo method (available in SAS 9.1 by specifying METHOD=NETWORKMC in EXACTOPTIONS) produces estimates of the exact p-values.