Problem with servers using F5 as DG

If I understand your configuration, it's a rare one; server trying to reach servers on the same network and in the same server pool as the requesting server. The SNAT should work but perhaps you used Auto-SNAT and the source is the same as the VS address (e.g. 10.1.1.1) which could cause the loop you are seeing. Try a SNAT, but use an address other than the VIP. Another alternative is to create a new VS with a VIP on the same network as the server (and pool members) you are trying to access (i.e. 10.2.1.x).

I have no idea what would happen if the requesting server gets itself as the destination in this scenario, seems to me you should put content on another IP address range on the same server or even on another pool of servers and make this a whole lot easier! All this looping back through the LTM can't be more efficient or better performing than just distributing the content to different IP addresses and using internal VIPs instead of pushing everything back through the 10.1.1.x VIP.