[Jerry Simcik]

Umm, aren't we overlooking the obvious?

It's your brake pads.

The inconsistent noise at first is caused by the pad's metal or warning tabs starting to rub against the rotor. When you apply the brakes, the force pushes the pad up against the rotor fully, which eliminates the noise temporarily. When you let off the brakes, it usually returns. It will be worse in the morning, especially if it's wet out, as there will be surface rust on the rotor. Over time, this noise will get more consistent, and much louder. It is common on older cars the that caliper slides freeze up, so while the outside pad may appear fine, the inside pad (which is harder to inspect) may be worn completely.

Check the brake pads. It's a simple check, and I bet it fixes your problem.

 

[Jerry Simcik]

Okay, if it's not the pads, did you also check the warning tabs and look for anything else that could be dragging or rubbing against the rotors?

I had this exact thing happen - though with another car - and it was the pads. This is why I suggested it.