It would depend on the quantity of the drippings and whether they were (mostly) defatted. Defatted drippings of just a few T per recipe would not significantly shorten the shelf life. A greater quantity, especially if containing fat, might lessen the life to 2-3 weeks.
If using homemade stock or dripping from a cook done ahead of the time of sauce preparation, treat them as you would meat, i.e., cool quickly and store in the fridge. With those protocols, shelf life is one of a quality issue, not a food safety issue.
An alternative is to freeze excess sauce in smaller quantities, either by vac-packing or in freezer containers.
Welcome to the board!