This was a couple of issues. We were not doing any split tunneling and the dhcp lease on old routers was set to expire every hour. Since we did not do the split tunneling, all traffic was sent down the tunnel and the lease could not be renewed. The tunnel would eventually drop, then the lease could be renewed and finally the network connect session automatically reconnected. To solve it we simply allowed access to the local subnet (not preferred from a security standpoint, but solved the issue). The second set of disconnects seems to be resolved with reinstalling the software.
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