The initial limit most banks floated to me was 10% of top-line revenue, but once they heard what topline revenue was (low to mid 6 figures), they generally suggested withdrawing the application and getting a credit card issued instead. I believe this is primarily because they thought it was unprofitable to underwrite the line of credit rather than an early denial for probable credit risk.
I ended up with ~$200k available on credit cards but couldn't get a line of credit through a traditional lender. Since I needed one, I ended up getting it through OnDeck, which charged 36% APRs. While I was not thrilled about that number, at all, it protected me from having to raid family finances to support the business several times.
(This product theoretically exists in Japan, too, but is extremely hard to access for SMBs without hard collateral like real estate to lend against.)