Couple of ideas:

Make sure your wrists aren't at a funny angle. They should be in a neutral position (the way they look with your hands hanging at your sides) for the majority of the time. Paying attention to that will let you know if you need to change your position or your stem.

Also, even though we all have a position we find most comfortable, it's important to change hand position for a little while every few minutes. Our hands and arms aren't meant to hold one position for hours.

Finally, don't grip the handlebars too tight. You don't need to exert any pressure to keep control of the bike. You should keep a light touch on it!