Is it a CR-2032 battery? Replace it if it's old and retry.

Usually the newer cars will tell you if the FOB battery is low, my 2013 Lexus does.

Moving on, take a digital multimeter, set it to 20 volts, measure the engine battery when the engine is off, should be at least 12.6 volts.

Start the engine, carefully measure again, should be 13.5 to 14.5 volts.

 

My Tacoma hybrid does not keep its 12 volt fully charged either. It only keeps it between 12.0 and 12.2 volts when the engine is off. It does jump up to the 13.5 - 14.5 range once it starts, and it always starts because it uses the hybrid battery to start the ICE. When I get the chance I will see what my dealer says, but a lot of people with 4th gen Tacoma hybrids have the same problem.

 

That's the battery in the fob.

The 12V battery has nothing to do with the range of your fob.

 

yeah i was kind of confuse, he was talking about the fob and others were taking about the 12v battery.

if you have to place the fob near the start button to start, most likely your fob battery is getting low.
just check with voltimeter the old battery, new battery should be 3.3V where old battery usually below 2,9v

i think i read somewhere saying that it is better to get those faraday pouch so you can block the fob sending signal. because if you park in your garage and the fob is close to the car, it might be sending or receiving signal from the car. specially if you open or close your car door.
this will short the battery life.

 

If there is any doubt about the condition of the battery in a key fob, just replace the battery.
It's not worth the time to crack open the fob and remove the battery to test it.
Open the fob one time, replace the battery and be done with it.
Keep a couple CR-2032 batteries on hand. It is a fairly common size used by a variety of devices.
Just be advised, the CR-2032 is a lithium battery that should be recycled not trashed.

Amazon - CR-2032 batteries