There are several things that can cause a deal to be canceled:

• The Customer (the one with the trash) does not have a minimum amount of money in the bank.

  Something like twice the cities TOTAL budget for a month. If you're out of money, your only option is loading from where you saved the city last, or taking out a loan. I have had this kill cities before.

• Service Provider (the one burning the trash) does not have enough capacity.

  Note that when you are playing as the Customer, the Service Provider's info is locked in: the capacity for each month and the total trash collected DO NOT CHANGE no matter how many months you play as the Customer. This means there's no chance the Service Provider's land fills are full, but rather that the customer is making too much trash each month for the Service Provider to take.

• The connection is broken.

  Simple enough, the roads/powerlines/pipes have been demolished due to a mis-click or disaster or something.

In any of these cases, the deal is canceled automatically. You will have to open both cities, check that everything is OK, THEN re-initiate the deal. Also, I believe you sometimes have to run a month in either city for any correction you've made (such as building more landfill) to be recognized, and allow you to restart the deal.

Yes, this is where the SimCity 4 save games are kept. To be on the safe side, I'd copy the whole SimCity4 directory from your Documents folder. I believe they're organized by region, and then within the region the individual saved cities are located.

This About.com article mentions backing up this folder in order to back up your SimCity 4 saves, and I remember copying this folder before when I played SimCity 4.