Multiple Budget Files Summary

I have 3 different budgets that feed into a single document. Each budget is maintained by a different person as a stand-alone file. Once a month, each person sends me their budget which I then paste into a "Master Budget" which has a tab for each budget.

I would like to create a budget code totals tab that calculates the total for each budget code so that I can look at how much money has been spent between all 3 budgets for each budget code in 1 place.

The problem I am running into is that since additional line items are added each month, every time I paste the updated budget into my master file the cell references will be invalid on my code totals tab. I also can't name the cells becuase I cant copy and paste the cells and take the cell name with them.

Is there a way around this?

I have attached a small sample file which hopefully helps illustrate what I am trying to do.

Thanks!