One thing is easy to spot. The RESET is not a response to a client-side time-out, it is the result of a server-side (or perhaps proxy-side) time-out.

Looks like your client is not noticing that it got a full response. After 60s of idleness, the server resets the connection. I would have expected that to be done via a FIN packet not a RST packet. Perhaps this is to blame:

If such a host actively closes a connection but still has not read all the incoming data the stack already received from the link, this host sends a RST instead of a FIN

But that would require a bug in the service, I think, which seems less likely in most environments.