Are you experiencing any problems? TCP Connections usually dont timeout unless they remain half open or just plain never get a fin packet. So the issue here could be a few things.
ddd.ddd.ddd.ddd == Destination
sss.sss.sss.sss == Source
This is what I suggest
Start a capture on the traffic in question. We want to do this from the source facing interface first:
access-list cap_http permit ip host sss.sss.sss.sss host ddd.ddd.ddd.ddd
access-list cap_http permit ip host ddd.ddd.ddd.ddd host sss.sss.sss.sss
capture cap_acl_http access-list cap_http interface inside buffer 8000
Attempt the traffic that is failing. After that is complete perform a "sh cap cap_acl_http" on the PIX. Copy and save the results.
Do the same on the outside interface. This time the source IP will be the nat'd IP on the outside interface
no cap cap_acl_http
no access-list cap_http permit ip host sss.sss.sss.sss host ddd.ddd.ddd.ddd
no access-list cap_http permit ip host ddd.ddd.ddd.ddd host sss.sss.sss.sss
access-list cap_http permit ip host sss.sss.sss.sss host ddd.ddd.ddd.ddd
access-list cap_http permit ip host ddd.ddd.ddd.ddd host sss.sss.sss.sss
capture cap_acl_http access-list cap_http interface Outside buffer 8000
Scrube the IPs in both captures and post the results.