I'm not familiar with the exact details of the shield you are using, but the W5100 ether module typically can buffer 3 or 4 1K byte packets at close to wire speeds, but the interface to the UNO is via a much slower SPI, so if your SPI can't keep up, UDP packets will be dropped in the ether module. If you want sustained, lossless UDP, you will have to throttle down your remote transmitting device to run at the much slower SPI speeds. You can experiment with various delays between packets on your remote transmitter to see what works on your receiving Arduino. TCP might be a better choice (just as slow or slower) but it adapts to available bandwidth and is reliable.