I have a customer's site where the XEP remains on the network with a static IP and static port config and at random times, while the unit is still pingable, RP will not connect to it (they use it often to add/remove user credentials for access control).
My own personal unit, with reserved DHCP address and static configuration does similar and/or my DNS stops updating properly (even with the service running on an external machine to update and ping the DNS server) and while RP can connect to it on the LAN, the WAN seems to fail occasionally. Might have to do with Uverse and their gateway. Too lazy too look into it further.
In a customer's situation, it's pretty easy to automate and tie into a consumer router/switch and modem to force a reboot remotely, same with the XEP. Far easier to do this as a troubleshooting step instead of rolling a truck. Same goes for most situations...customer on vacation but can't get their app or what have you to connect remotely...easy enough to dial in (yay POTS!) and do a remote reboot.
Usually I'm putting in a M1RB or XOVR or both and usually have spare outputs to burn. That and a DPDT relay can be pretty easy to do.