it is UDP?
my EthernetENC library has a backlog for UDP. UIPEthernet doesn't. The size of the backlog is configurable with UIP_UDP_BACKLOG
https://github.com/jandrassy/EthernetENC/wiki/Settings
and you can turn off TCP with UIP_CONF_MAX_CONNECTIONS to save flash and RAM.
and you can set more frequent network handling with UIP_PERIODIC_TIMER