The water will cut off from the shower head until I push the diverter down and lift it again

Sounds like a bad spout to me.(see image). These spouts are so inexpensive that we don't repair them. We simply replace them. There are two types of diverter spouts. The threaded type and the slip on type. To tell what you have look at the bottom next to the wall. If it has a small square opening then you have the slip on type. Pick one up at any big box store and replace your old one. Good luck, Tom

Sounds like a bad spout to me.(see image). These spouts are so inexpensive that we don't repair them. We simply replace them. There are two types of diverter spouts. The threaded type and the slip on type. To tell what you have look at the bottom next to the wall. If it has a small square opening then you have the slip on type. Pick one up at any big box store and replace your old one. Good luck, Tom

I replace the spout with a brand new one on Friday, it worked well Friday night but back to the old trick on Saturday morning

Are you on a well or city water, Any problem with the aerators clogging up? Have you removed the spout and ran water in the spout end to back flush it? Let me know, Tom

Are you on a well or city water,? Any problem with the aerators clogging up? Have you removed the spout and ran water in the spout end to back flush it? Let me know, Tom

I'm on city water, and I don't have any aerator problem, I'm wondering if the whole faucet system is bad

This is the same spout as the one I put up isn't it? A spout diverter works on pressure, You turn on the tub valve and then pull up on the knob. This closes a plate that prevents the water from coming out of the spout. As long as the pressure's on the diverter will remain in the upper position. If it can no longer exit out of the spout the pressure will force the water up the shower raiser and out the shower head. This is how a diverter spout works.

When the shower cuts off does the flow stop at both the shower head and them spout or does it just stop the shower and then comes out the spout? Have you removed the shower head and then tried the shower?
Let me know, Regards. Tom

This is the same spout as the one I put up isn't it? A spout diverter works on pressure, You turn on the tub valve and then pull up on the knob. This closes a plate that prevents the water from coming out of the spout. As long as the pressure's on the diverter will remain in the upper position. If it can no longer exit out of the spout the pressure will force the water up the shower raiser and out the shower head. This is how a diverter spout works.

When the shower cuts off does the flow stop at both the shower head and them spout or does it just stop the shower and then comes out the spout? Have you removed the shower head and then tried the shower?
Let me know, Regards. Tom

Yes it does Tom stop at both spout and shower head

Remove the shower head. Does it still cut the flow off from the spout and open shower am, Let me know , Tom