Nojan,
I setup a similar scenario utilizing firbug with firecookie enabled.
Browser1: http://.company.com:/... - this is the URL utilizing the DNS alias that the f5 BIG IP listens on
Browser2: http://.company.com:/... - this is the URL directly to the app server
I can see that on Browser1, when left idle for 10 minutes then clicking a link, the SAP cookie (saplb_*) changed values to a different J2EE instance and server node and displayed the 500 error.
On Browser2, when left idle for 10 minutes then clicking a link, the SAP cookie (saplb_*) remained the same value and worked correctly displaying the results of the link.
I know that source address affinity was selected as the primary persistence on the BIG IP. Looking at the guide, I see that Cookie persistence is recommended as the primary and source as the fallback. Unfortunately these settings were chose before I came across this guide myself. Do you think changing it to cookie persistence as primary could resolve the problem?