When an order is made, or a recurring service is being billed, an invoice is sent to the client with payment details. An invoice could be a simple e-mail instructing the client to pay funds to the hosts PayPal account via the PayPal interface, or a payment button on an invoice which links directly to the PayPal page.

When the client makes the payment, the host automatically (or manually, depending on whether or not a billing system is used) register the payment and the service is extended to the new due date.

So this seems clear, what can go wrong with this?
Well, there are three parties involved.

1: The host, which sends the invoice, waits for and register payment, thus extendnig the service.

2: The client, which receives the invoice and makes the payment.

3: PayPal, who transfers the payed amount from the payer (the client) to the receiver  (the host), and then, if the host has this set up, send payment notification to the host.

Note that the host cannot charge or bill the client. The PayPal system doesn't work this way. It is always the client who initiates payment.

In the above scenerio, it is quite possible that the host simply does not check its PayPal balance, thus never knowing that the payment is received. But this does not result in double charge. Remember the host cannot in any way draw funds from the clients PayPal account. The host may very well send invoice reminders, and suspend accounts in worst case.

So when does the problems start?

The big problem is the PayPal subscription feature.
The subscription feature was created for people that makes regular PayPal payments to other people or companies. Perfectly suited for recurring amounts, such as web hosting. The PayPal subscription is also initiated by the client, not the host, and it can only be cancelled by the client. With some billing systems, the host can not even see that a PayPal subscription is in place, nor see the date on which the next payment will be received.

Whenever a payment is made with PayPal, the payer is given a subscription choice.
If a subscription is created, PayPal will transfer the amount every month on the date that the initial payment was made. Some hosts provide two PayPal buttons on the invoice or e-mail, one for the normal PayPal payment, and one for the PayPal subscription option.

In the PayPal subscription scenario, it is PayPal who transfers the funds according to the payers wishes. The host is only receiving the funds.

So now we have two parties responsible for transferring payments. The client making PayPal payments manually, or PayPal making the payments regurlarly according to the clients wishes.

With PayPal subscriptions, the invoice gets obsolete. The sum is always the same every time, and PayPal transfers it to the host without interaction from the client. But again, the host may not know that the client uses a PayPal subscription to pay the invoice. Some hosts suspend sites pretty quickly on non-payment, and reminds the client a few days prior to the due date that it is time to pay the bill.
The client recieves the invoice reminders, thinking that its overdue, or forgetting about
the PayPal subscription, and pays it. A few days later, PayPal makes the transfer according the the subscription, and thus the host is payed twice.

This has been the case in 4 out of 5 times when someone has approached me with this problem. It's not the host who charges the client twice, its the client who pays the host twice.

There is another feature that complicates things even more. Remember that the PayPal subscription payments are made automatically every month on the same date that the initial payment was done?  Then consider what happens if the initial payment was made overdue.