But that is not consistent with a steady current drain of only .5A. Possibly the method of measuring current is not right?
kbrandt: How are you measuring the current? Clamp-on meter? Might there be a problem with it?
If you put a heavy load on the circuit (like a 1000W heater) does the breaker trip sooner or does the time remain about the same?
Can you measure the current with the heater (or some other known load like a 100W lamp) plugged in to check your measurement?
The only time I have run into a circuit tripping but have a low value current reading was because of a flashover arc that would cause it to trip, most of these were because of damage underground UF circuit in dry soil, but they would not constantly trip, maybe a day maybe a week would pass before it tripped again, I have also had it happen from taped splices when the hot and neutral splices were taped into the same bundle, moisture had gotten into the splice and after a few arc overs it would leave a carbon trail through the tape that would flash over from the smallest transient spike, one was in an attic that a bare hot and neutral was against the wood rafters, after I guest some time it cause what is called pyrocarbonization, a carbon track would form between the two conductors across the wood that would flash over, the only thing that saved it from causing a fire was the breaker was very weak and very sensitive and would trip, it was just a few steps away from causing a fire, In most of these cases it took a megger to find the problem as the resistance was so high most ohm meters would not show a problem.
One case was kind of strange until I understood what was happening in the flashover caused by a transient, the home owner told me that every time his AC unit shut off or his wife went to turn off the vacuum or some other motor loads it would trip the breaker for the livingroom, it would also trip after a good soaking rain, in checking out the circuit I found it fed the post light off a foyer switch which was also on with the living room circuit, when I used an ohm meter it didn't even read anything (of course it didn't rain that day go figure) but I did disconnect the post light and the problem went away, I borrowed a friends megger and it showed right up, using my underground locater with the A frame to locate the fault I dug up the bad section but didn't take it apart, I had the home owner turn on and off his vacuum and sure enough it would cause it to arc every time he turned the vacuum off, it was truly an eye opener.
Not saying this is the problem but worth checking if you have a megger as for cases like this its value is worth every penny spent on a good megger, after the above I got one for myself as it is an invaluable tool for trouble shooting, much happier customers when you can go right to a problem or at least show there is a problem with a circuit when all other testing shows its good.
Another point of advice is to know how to tell the difference between an overload and a fault, knowing how a breaker operates can be one of your best friends because it can tell you what type of fault is causing the tripping, an overload will cause a breaker to trip after some time, also you should notice that the breaker wont reset till the element cools down so if a breaker doesn't reset right away you know you had an overload, a dead fault will cause the instantaneous magnetic pickup to trip the breaker, this will not heat up the bi-metal trip part of the breaker and it should reset right after the trip even though it will trip again, while I don't condone using this method yourself as it is not a good idea to reset a breaker into a fault until the problem is found, most times the homeowner has already tried to reset the breaker so asking them some simple questions, like do you have to wait a few seconds before the breaker will reset or does it reset right away can give you the info you need without having to do it yourself which is much safer for you as well as the liability of causing a fire, as you will never know if the breaker contacts have welded or the fault is a open splice that has already started arcing close to combustibles.
I know it is common and I have seen it even in trouble shooting books that tell you to remove all known loads then try to reset the breaker, which is very wrong and dangerous, it should tell you to remove all known loads and test the circuit with an ohm meter to see if the fault is still there, if it looks like its gone then break out the megger and test it again, then and only then do you reset the breaker, then test each load with the ohm meter to see which one was the problem, this is the only safe method to use.