The customer chose a point, and then the delivery option is either missing at checkout or arrives without the point code. This is a different problem from a missing picker.
No rate is mapped. On the Delivery method card of the General tab, the carrier must be ticked and a real rate chosen in the list under it. With no rate mapped, the app leaves your checkout alone.
The rate never reaches this cart. A rate in a shipping zone that does not cover the address is never offered, so there is nothing to rewrite. The same goes for a carrier-calculated rate on a store with no active carrier service. Pick a rate with a fixed price.
A visibility rule excludes this cart. Rules on the Pickup point visibility card remove pickup delivery and cash on delivery together. Retest with a plain, cheap, light cart.
The customer chose Other delivery option. With Hide pickup point delivery at checkout ticked, pickup delivery stays hidden for the rest of that checkout, including pick-after-purchase. That is the setting working, not a fault.
Both carriers are enabled. Choosing a point of one carrier hides the other carrier's rate, which looks like a rate disappearing.
You are over your monthly limit. The badge Limit reached on Plans confirms it. Your pickup rate keeps its plain Shopify name with no point code, and the cash on delivery rate is offered in every cart instead of only after a point is chosen.
Reproduce with one product, one country and a plain cart before changing settings.
If the rate appears with no point code, the customer did not complete the picker: What the app writes on your orders names the tag.
Renaming a rate in Shopify breaks the mapping. Punctuation, spacing, capitalisation and Polish accents do not matter, a changed letter does.
Stuck on any of this? Open the chat in the bottom right corner of the app and we will help you set it up.