The Panel Designation CH24CCR is a Main Lug Only Panel. This means it doesn't have a Main Breaker and looking at your meter location and nipple running into your panel, there is no enclosed main breaker or fused disconnect. They do make a main breaker kit but you would have to find a cover with a hole for it. Looking at your photos I would say your best bet would to replace the panel with the correct configuration.
As far as your dryer circuit goes. When you reset and run your dryer does the circuit breaker get hotter than normal? It should not really feel hot to the touch. If it is heating up you may have a damaged breaker or lugs and it's slowly heating up enough to trip the bi-metal device inside. It will continue to weaken until and trip more frequently as time goes on. That sounds something like you are experiencing. It might also be a loose connection at the breaker lugs, but if it is tripping the breaker, I would bet it is already damaged. So you might see about replacing the breaker make sure you clean the conductors and follow the torque table on the label when tightening up the conductors.
The only real way to verify that it is the breaker or an overload is if you have an ammeter. you can check both conductors coming out of the breaker and see is the amperage is too high for the circuit. If its pulling less than 21A the dryer is operating ok. Leave the ammeter on the circuit and check back from time to time to see if the amperage is changing before the breaker trips. The more expensive ammeters will have a peak amperage button so you can check and see if the current spikes while in use.
Remember you will have to be checking amperage's while the power is on. So exercise extreme caution while testing. If you feel you are not experienced enough then seek qualified help.
good luck and stay safe.