When the option actually appears
The redirect option only exists once DPD has scanned the parcel into their network. A retailer's dispatch email arrives well before that, sometimes a full day before, and during that window DPD's tracking page just says they're expecting it. Nothing you press will redirect a parcel DPD hasn't got yet.
Once it's scanned in, the option is usually open until the parcel is loaded for delivery. On a normal week that's an evening. On a busy drop week, when the depot turns parcels around overnight, it can be a couple of hours.
Why resellers miss it
Because the window opens at an unpredictable time and closes fast. If you've got eight parcels landing from three retailers, you'd need to be checking eight tracking pages through the evening to catch each one at the right moment. Most people check once, see "not available yet", and forget until the driver's already been.
The other trap is the postcode. DPD verifies the recipient with the delivery postcode, and a typo or an old postcode locks you out of the redirect for that parcel after a few attempts.
What a good setup looks like
Pick the shop once. Every parcel to that address goes to the same shop, so the choice should be saved, not made per parcel.
Let something else keep an eye on it. Once DPD has the parcel, the redirect gets booked and the confirmation and collection code land in your email. You never open a tracking page.
Have a second and third choice. Parcel Shops go full or close early. If the first one can't take it, the booking should fall through to the next one on your list without you being involved.
That's what Minted's parcel tracking does for members: your DPD parcels go to your saved shop as soon as the option opens, and they stay on your tracker marked as redirected, with the collection details attached.