Long pre-heat cycles can have more than one cause.
Make sure temperature sensor in contact with the print bed.
Double check the connections between the controller and the heated bed. If a terminal is not screwed down securely on a bare wire it could reduce the current going to the heated platform. This can result in burning out a connector.
I'm not familiar with the davinci firmware but If you can
run a PID calibration on the heated bed, you may reduce the time needed for pre-heat. This is a simple g-code driven calculation on arduino based printers using marlin firmware.
This post may help:
http://reprap.org/wiki/PID_Tuning
I've had one other instance where the heated bed got to temperature but would not start the print for a random amount of time. Sometimes the print would start in 10 minutes other times it took 50 and others it never started. If your print start time is more random, I would suggest looking in your firmware for settings similar to the one below.
// Actual temperature must be close to target for this long before M109 returns success
#define TEMP_RESIDENCY_TIME 10 // (seconds)
#define TEMP_HYSTERESIS 1 // (degC) range of +/- temperatures considered "close" to the target one
The random start times was caused by the "RESIDENCY" set to "10" with the "HYSTERESIS" set to 1. So the bed had to hold its temperature within 1 degree for 10 seconds before the print could start. We were printing ABS and with the bed temperature set to 110^, the fluctuation was more than 2 degrees.
After the printer was run through PID tuning it was able to hold a temp to +-1^, but it was still faster to start printing when the the "RESIDENCY" was changed to "2" and the "HYSTERESIS" set to "3".
// Actual temperature must be close to target for this long before M109 returns success
#define TEMP_RESIDENCY_TIME 2 // (seconds)
#define TEMP_HYSTERESIS 3 // (degC) range of +/- temperatures considered "close" to the target one
Try the PID tuning first, this will most likely solve the problem before you have to get into anything deeper.