5 years ago we had a hot tub installed; worked fine until a couple of weeks ago, it was getting no power; repairman came out and fixed it and said that we should upgrade from a 100 amp breaker box to 200 breaker box. My question: if this is true why did it work fine for 5 years?

It could have worked at a borderline for a few years, but should be at the correct amperage now.

Is the repairman an electrician? Is he qualified to calculate the maximum electrical demand?

Calculating the maximum potential load is a bit complex, taking into consideration the size of the home, the kind and number of high use appliances such as electric water heating, electric cooking appliances, electric heat and air conditioning.

Has your main breaker ever tripped off due to overload?

The size of the service entrance panel will have no affect on the operation of the hot tub until the total usage in the home exceeds 100 amps. At that time the main breaker would trip off.

The size of the service entrance panel is not the source of any problem with the hot tub.