Why is it taking so long for a payment to come through from a credit card paid directly through emailed invoice?

Hi katlinstolz-gmai.

Making sure you get your payments sent to you in a timely manner is what QuickBooks Online Payment add on is all about. I'd be happy to help you with getting the funds sent to your bank.

Normally the payments are deposited after 2 business days or 5 for your first transaction. If the payment still doesn't show up after that time check the payment entry in QuickBooks by going to Sales>Customers and selecting the customer that made the payment. Once you pull up the payment transaction it'll say if it didn't go through. If it went through but the payment still hasn't been deposited after that time I recommend contacting our payments support team so we can pull up your account and see what's going on. You can reach them using one of the following methods: 

Schedule a Callback or start a Chat: click (?)Help in the upper right in QuickBooks Online > type and enter "Contact support" into the QB Assistant > click Contact Us > explain your situation > click Let's Talk > choose Get a callback or Start a Chat.
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Support hours are from Monday to Friday between 9 a.m. and 8 p.m. ET.

Have a great day!