Collecting by hand only works if not paying has a consequence, and the consequence is access: stop paying, stop training. A contract with an invoice left overdue about a week past its due date stops covering new bookings, and the member is always told why.
That asymmetry is on purpose. Blocking somebody who paid an hour ago is a furious phone call and a front desk that stops trusting the system; being a few hours slow to block somebody costs one class.
The block sits on the contract that owes, so a member paid up on personal training and behind on their membership keeps the training. Only contract-linked invoices count: a t-shirt or a drop-in that goes unpaid chases by email and never withholds anything.
A blocked contract is still active. It is a payment problem, not a cancellation, and pausing or ending it is a separate decision described in Pause, cancel or end a contract.
“Settle it by Friday and keep training” is a thing every gym says, so it is a thing the contract can hold. Open the contract, choose Extend deadline and pick the date. Access is not withheld before it whatever the grace period would have said, and granting it lifts a block that has already landed.