Thanks for your post. Apologies for the late response.
Can you provide some additional detail? Since this is an intermittent issue, it would be helpful to narrow down the possible causes.
Does the connection not succeed at all, or does it hang once the file is opening? Is the user account and computer for the same person each time, or is it also random? About how many clients access this particular file via Instant Web Publishing; are there clients that never have a problem with time-outs? Is it restarting FileMaker on the client that permits the connection to persist? Are all the clients on the same type of hardware and OS?
Since it has been some time since your post, if you have resolved the issue, please post here so that others having a similar issue might benefit.