In the dilute amounts that you are supposed to use this product it would take gallons to affect your soils pH.
As long as a tomato plant is protected from frost it will keep on growing forever, provided its food and water needs are met.

I have used Neem for years (dyna-grow brand) and it has never been anything but the best thing I have ever discovered. I quit using anything else and my ph is always right on. Go purchase (for about 7$) a little ph/moist meter. ph for tomatos is 6.0-6.8. If your soil is too alkaline then sulfur helps if your soil is too acidic limestone is the best but dolomite is good also.

The formula I use for neem is 32oz. of water with 2 capfulls of Neem. ( i use the 8oz. jug of neem).

Tomato plants literally just give up the ghost when they are done. Tomato plant are what they call tender perenials and they grow as annuals. that is why you have to plant new ones each year. they either do a 4-6 week growth and then die or they let the frost get them. It depends on the type you plant.