Bring the handset that says searching into the same room as the base and see if the handset stops searching. Next unplug the handset batteries (yes from all handsets) and the base power cord (from both the base and the wall outlet). Wait a few minutes and then reconnect the batteries and base power cord. Next try to de-register and then re-register the handsets. (If you add a comment with the phone model, I'll help you with this step. Uniden has the manuals for their phones on their site: http://www.uniden.com/bin/venda?ex=co_disp-view&bsref=uniden&scat=dectphones_mnl
If this doesn't help, next try a new battery (and make sure that the battery is fully charged) for the phone. (If the phone is under warranty, contact Uniden. Note: batteries lose their ability to hold a charge over time. This includes the time on the shelf in the package.)
If a new battery doesn't help, then there is something wrong with the handset. Decide if it is worth having the unit fixed if the phone is out of warranty.
I hope this helps.
(I'm assuming that both handsets are cordless. If you have a corded/cordless model, then check that the base has power before you go farther with the above diagnostics. The power brick should be warm. We had a cordless phone on a power strip (UPS) that got turned off. The handset was searching for a signal that wasn't being sent. If you have power to the base, try sending the Find Handset message. The problem could be either the base or the handset not sending and receiving the signals between them.)