A digital thermometer runs on a battery. If it's on all the time, the battery will run out faster and respond slower. If you can turn if off, do so, until you need it. Assuming the battery is fine, it shouldn't take more than 10-15 seconds to get an accurate read.
The 'regular' ones have a tiny spring coil that moves the indicator. Little should interfere with it's movement, unless it's been dropped or if moisture has gotten in... That one, also should take no more than 10 seconds. This one you have to calibrate often with an ice bath method.
How can we sleep while our beds are burning???