This happens frequently with my server also, which is on a Gigabit Ethernet LAN connection to the client. Server is vanilla (no mods) 1.8.8 on Ubuntu Linux, the hardware is a little old (Athlon 64 with 3GB RAM) but seems to get the job done. Clients are late-model Macs running OS X El Capitan with 16GB RAM each. If I were to guess, maybe the timeout before the Minecraft client considers a server to be "offline" needs to be bumped up a few tens of ms.
This happens frequently with my server also, which is on a Gigabit Ethernet LAN connection to the client. Server is vanilla (no mods) 1.8.8 on Ubuntu Linux, the hardware is a little old (Athlon 64 with 3GB RAM) but seems to get the job done. Clients are late-model Macs running OS X El Capitan with 16GB RAM each. If I were to guess, maybe the timeout before the Minecraft client considers a server to be "offline" needs to be bumped up a few tens of ms.