The first message indicates ISAKMP processing. There was an ISAKMP packet with source address of his FW and destination address of your FW. The source port and destination port were both 500 (UDP 500 is the port used by ISAKMP).
The second message indicates that you received a Dead Peer Detect message (DPD) which is a method for determining whether the remote peer is still working and responsive. If DPD does not get an appropriate response from its remote then it will tear down the Security Associations.
I do not know if this gets you closer to the reason why you are getting disconnects from your peer. But this is what these messages mean.
HTH
Rick
HTH
Rick