Steve,
This could be very simple or difficult to diagnose especially from a keyboard at a distance. I'll give you some scenarios that may help conclude your repair.
1. The main has weakened over time making it overheat and trip before the branch circuit breaker.
2. The branch circuit is faulty and may never trip on overload resulting in the main overheating and tripping instead.
3. The main has a lower AIC rating than the branch circuit breaker and will always trip first. My first move is to check these ratings to make sure they are coordinated so this doesn't happen.
4. The terminations at the main either at the lugs where the service entrance conductors terminate or the bolted connection where the main ties to the buss.
An ounce of prevention is worth a pound of cure. If the ratings of the breakers are coordinated I would definitely replace the branch circuit breaker. I would never tell you to try any of the techniques I use to tighten the lugs at the line side of the main. You need to de energize the service before attempting that. Add some penetrox to these connections if you are able, it's an anti corrosion grease that's about $12 a tube. All our meters are digital and have a tamper proof ring but if the meter is removable and is, the power company gets an alarm and shows up to see why the power is off. I recommend setting up an outage with them to perform the lug tightening and inspection or main breaker replacement if that's what you need to do.
AIC ratings are listed on the side of the breakers in 10K, 15K, 20k, 25k etc. etc.
If the main is rated at 10K AIC and the branch breaker is 20K the main is probably going to trip first in a fault current situation, i.e. short circuit. Overloads are different, the breakers are a thermal sensing device and trip when they overheat in a predetermined time.
Try swapping the trouble branch circuit from the breaker it's currently on with one that doesn't get much use and see if that cures the problem. If it does, replace the problem breaker.
I hope this helps and please make sure to deenergize anything you work on so we can continue participating with you here on OPP.

zombietracker

No one realizes the true costs associated with their little electric death traps, they all just talk a good game. At minimum you'll need a 50 amp, 240 volt circuit to run the charger. Is your electrical service a 200 amp already? No, I didn't think so. If I come out to upgrade your service from 125, 150 amp to a 200 there's a chance it'll run ya min. $2000.00. If the service is fed from underground and I have to install larger service conductors, 2/0 copper, 3/0 aluminum it's more depending on the length and if I have to dig a new ditch to install it. Could be up to $5000.000!
These greenies never consider the cost of that little electric car they're going to buy and never consider where the energy comes from. So he lives near a gas generator plant, it's connected to the national grid. If we were to shut down the coal generators none of the alternate sources would be enough so all goes dark. His car won't run without him pushing it.
They do talk a good game, how long is it going to take for that little battery box on 4 wheels to pay for all the upgrades done to charge it? They don't know, they have to replace the batteries soon enough to. Those don't last forever.
Have them tell you of the toxic mess the disposed of solar panels are creating as they don't last forever either.
Lightning! No one ever considers the damage caused to P V electrical systems by lightning strikes. It's a cost game changer no solar system buyer ever considers as they cream their shorts having one installed so they can go green.
Ignorance is bliss as shown in our example with permadumb.
There's so much more than just buying the damn electric car these green pukes never consider.