Most often the problem you describe is with the thermo … system. Here are a few things to start with:
Does it have a thermopile or thermo couple?
-If a thermocouple, make sure the retaining clip is installed(in addition to the retaining nut). As the oven heats up, the thermocouple wire expands and bends and if the clip isn’t installed, the probe can pull back out of the retaining nut and away from the flame. This is often the case in the situation you describe.
-Also, when you adjust the pilot flame, does it turn up and down as the pilot adjustment screw is turned. If it doesn’t turn up as high as your other oven’s pilot flame, the pilot orifice could be clogged. Take orifice off, hold up to light to see hole size, blow out with air from both sides. Often you can see the hole size open up after the air blow in the case of clogging. Reinstall and hope for larger pilot flame.
-Check the pilot flame supply line for leaks. The pilot flame supply line can become loose or corroded and if leaking can cause the pilot flame to be low. Most likely side to leak is pilot flame side and as the oven heats up, metal expands and the leak can become larger thus diminishing the size of the pilot flame.