Nimbostratus
EmployeeIf you have a widieip www.site.com - pool A - serverA - pool B - serverB
At the wideip level there is no fallback method. So, you may have Round Robin at the wideip level which means GTM will round robin requests between pool A and pool B. Then, in the pool, there are 3 levels of load balancing: Preferred, Alternate, Fallback Defaults are RR,RR,Return to DNS
In that configuration, Return to DNS should only ever be used when all the pool members are marked down (red diamond) or "unknown" (blue square). In your two pools, what are those 3 methods set to? I've seen a scenario where I'm using two dynamic methods as the first two and Return to DNS as my last and if GTM doesn't have enough dynamic info to make a decision, it drops down. If my pool members are generic hosts and I pick "Least Connections" and "VS Capacity", then Return to DNS. Those first two require intelligent Communication with an LTM instance. So, it doesn't have enough info to make that decision and will drop to return to DNS.
You should look at your log files and see if you have any of those pool members flapping (going from green to red and back).