Many things can happen after 10 years
- alternator not producing desired voltage and current to charge the battery to maximum (float charge)
- Electrical wiring (ground, main) have poor connection
- If self-start is working after the car cools down then it doesn't need to be serviced
How old is the battery, if more than 2-3 years, replacing it will solve the issue completely sometimes.
It is better to buy a brand new alternator and battery + wiring after 10 years (as a preventive maintenance) but if budget is low then just go for repairs/servicing.