I found this topic a few days ago while having the same problem with my new debit card. I later managed to get it added, and thought a detail or two of that might be relevant to someone.
My switch from the bank that's closing down is almost completed, I've been running down my old current account, and this month there wasn't enough left in it for our essential top ups (my phone and our router).
I'd seen one or two mentions here of phone top up not working. After some failed attempts at my3 (and knowing by then that adding a new card requires first topping up with it), I tried via 1913. It's fiddly, with our weak mobile signal, but needs must. (Driving to a town for voucher topup is just too disruptive, and I don't know if it works for routers). I used the 'different card' (or similar) option, and heard the option to save the new card details (I can't remember if it was before or after the topup, which was successful). But it was so long since I'd needed that option that I was used to just ignoring it, and realised too late that I'd heard it, so back to square one. Twice. (I was just thinking I might not the only one who's missed it).
I repeated the process for the other topup (also successful), and went back to my3 to see if it had made any difference there. It had been updated accordingly (very quickly; maybe instantly), reflecting the new balance and showing the new card as an option.
Another thing during that session is that (as sometimes happens), the start of the call was different from what I was expecting. It starts something like 'Our offices are closed at the moment', then goes on to suggest other ways of topping up. In the past, I've just tried again later, assuming something at Three's end was preventing the topup. This time I tried hanging on to hear the whole thing. It seemed to come to a full stop, but then after a short pause I heard the same options I usually hear at the start. (Can't remember if that was the phone topup or the router one, or if it makes any difference). I'd guess it's the normal message after office hours, but I hadn't spotted the connection, as I don't need to take them into account much these days. Maybe I'm not alone in having been put off by it.
It also took me a while to realise that if the old card is the only option showing at My3, we need to add the new one before we can remove the old one (which I wasted some of the My3 sessions trying to do). Though maybe that's irrelevant, if the new card has to do its first topup outside My3, and that always adds it automatically?
