How long will leftover pasta sauce keep?

It depends. Assuming it is refrigerated in an airtight container,  pasta sauce will keep for  5-7 days.
 
Generally, refrigerated leftovers--such as lasagna, spaghetti and the like--should be consumed within 4 days. Do not repeatedly reheat items such as lasagna. Each time the dish is reheated, it is subjected to temperatures (typically, 40°F-140°F) that promote bacterial growth.  In time, the dish may collect bacteria in numbers sufficient to cause spoilage, regardless of the temperature to which it is cooked. Microwaving alleviates the problem, but tends to dry out  lasagna and other casserole-like leftovers. Additionally, wheat products such as pasta tend to turn mushy when reheated in a microwave.
 
Freeze leftovers rather than repeatedly reheating them.
 
Source(s):
Canadian Food Inspection Agency "Food Safety Facts on Leftovers"