Fortunately the cash replenishes quickly but the time never seems to.

A cash-out refinance sounds better than the HELOC+mortgage combination on the first property.Item #3 looks like it can give you a very fast cash replenishment. $120k in profit, meaning you recover your equity, repay all the debt and repay whatever the cost of the rehab sounds like a great return.

I then deposit it to my business account or to replenish petty cash.

You will replenish your credit card borrowing capacity. 

Do they also refill/replenish things (TP, paper towels, etc.)

If i get to the point I need to replenish because I dipped below that level, I stop taking a monthly check and refill the buffer.I use this spreadsheet to account, it came from BP library but I corrected a lot of the formulas and look up tables and added several lines for income.

Now that we had our HELOC replenished we began searching for another property to invest in and we found a house that was ideal for a flip.

The first one charged one month’s rent to locate a tenant, required a $1000 deposit for future repairs that I would not even be notified about in advance, and would be replenished from the following month’s rent along with 10% management fee before I ever got any funds.

After investing in a few properties, even with cash flow, it'll take some time to replenish my cash reserve.

We all have reserve funds to deal with the very issues you are experiencing and when used are then replenished over time through our positive cash flow.