User1073881637 posted
Sounds like the backend resource is the cause or connectivity to the remote resource. I'd scour the iis logs looking for patterns with long time-taken
Here is a sample syntax using log parser.
logparser -i:evt "select top 100 date, time, cs-uri-stem, cs-uri-query, time-taken from <website.com> order by time-taken DESC" -o:csv
Or path to a specific log file
logparser -i:evt "select top 100 date, time, cs-uri-stem, cs-uri-query, time-taken from C:\Windows\system\logfiles\w3svcXXX\exXXXXXX.log order by time-taken DESC" -o:csv
See if you can find a pattern.