Big Green Egg Remote Wireless Thermometer ET-734

That unit is made (marketed) by Maverick under various names, I think.  The most common brand is RediChek.  Search this site for RediChek and read all about it.  My RediChek instruction say to turn on the receiver first and within 30 seconds, turn on the transmitter.

I offer two other suggestions:

First, remove the batteries from both units for a few minutes and let them reboot.  Then try again.  It worked for me when my cell phone was doing crazy things.

Second, it's possible that water/moisture has gotten into the probe(s).  The solution is to place them in your household oven at ~300 for a hour to evaporate any water.  Just heat the probes and cable, but not the plastic plugs.

Other than these, I can't offer any suggestions.  Good Luck.