Julie, two quick rules of thumb lenders consider, at application for purchase money they want to see 6 months PITI and 10% of the home value in reserves or enough consumer borrowing power to borrow for emergencies, to get them at that 10% level......that has room for +/- and isn't a "requirement" but a "like to see".

That will give you a really big cushion for any mistakes or emergencies:)

For my situation, I have a 10% interest rate on my HELOC, so I look at it more like an emergency fund, or a hard money loan that I would just use for a short period of time.

I would hope to have savings/ emergency fund set aside if something broke at the beginning.

Over the past few years, several larger private lenders have emerged that will lend to real estate investors (rental businesses and flippers), but they are going to be a bit more expensive than the bank.

Just have emergency contact info for them (or any tenant).  

My general question is how much should you have saved up in reserves to pay for large ticket, "emergency" type items on your properties? 

A good book regarding research on a national level for multi-family is "Emerging Real Estate Markets" by David Lindahl.

Do you have adequate savings in case of an emergency?

While signs point towards a recession (inverted bond yields, for example) growth and inflation remain strong (while less strong, of course, than just months ago), as does the general majority of emerging economic data.