The problem is reproducible. Was online in the wifi where server is reachable directly, server went into arp cache. Disconnected from said wifi, connected to other wifi. Server still in arp cache, now as
<incomplete> on wlan0
and therefore, again, unreachable under that IP address.
So at least on this Droid4, arp cache handling is definitely b0rken.
Note: if anyone else can reproduce this, I'd be happy to hear about it.