The Balance Sheet must always balance! Formula Asset = Liabilities + Equity, so think of it this way, you have a house, that house is an asset worth $100,000, if you get a mortgage of $80,000 (the debt), the remaining $20,000 has to go where? Well that belongs to you, which is in the form of equity. So when theory (Assets (100k) = Liabilities (80k) + Equity (20k) becomes reality is when you sell that house, you will pocket the 20k. Let's say now some time went by, and you paid off 10k on the mortgage. Well let's demonstrate what happens. The asset is still worth 100k, the liability (mortgage) is 70k, now where does that remaining 30k go? Well that's your equity. You see why it must "always" balance.
Now, in the context of the financial model, the revolver balances the model - think of it another way: say you make $100 of income this month. But you spent $120. The $20 difference is charged on your credit card (revolver). Next month, you make another $100, but you only spent $92. You have $8 of excess cash that 2nd month, which you will use to pay off your revolver of $20, leaving a net balance on revolver of $12.
A third way to explain it: As long as every item that changes on the IS and BS is reflected on the CF, you should balance. Why? Back to old school debits and credits and double-entry accounting. There's ALWAYS two entries for every transaction. Now, every item on the IS is reflected via Net Income and Retained Earnings via S/H Equity and Cash Flow Statement. So that takes care of IS integration. Go line by line thru the rest of the BS and you'll see all the working capital items reflected in CFO. Stuff like PPE is connected to CapEx (cash down), etc. Then, the Equity changes are reflected in CFF, leaving debt and revolver to cap off (see above paragraph).
Re: your iterations question - at some point the numbers don't change b/c Excel only calculates 15 decimal places. If Excel were to suddenly chanage that to 30 decimal places, then it would keep going and the numbers would change again. However, that one-gazillionth of a decimal difference has no material impact on our model. We usually observe no more than 30 or so iterations to balance, so a few hundred would be quite a bit actually.