This custom may be related to Biblical piety. In the Holy Land you can find a shrine over the spring that issued from the staff of Moses and the Well of Beersheba, and, if I remember correctly, Moses well near Mount Nebo. The Jordan was also associated with miracles, such as the healing of Naaman the Syrian, who had leprosy.
Reformation-supporting governments destroyed wells and springs associated with Catholic saints, including the most famous one in Britain, the Holy Spring of Our Lady of Walsingham.
Modern historians are increasingly questioning the Reformation assumption that these were originally pagan wells. There's a book from around 20 years ago called "The Pagan Religions of the Ancient British Isles" which debunks the idea that these were taken over from the Druids and so forth.
Oddly enough, just as modern historians and archaeologists are to some extent disproving that these wells were sites of Druid rituals, modern-day pagans are claiming them. But they are so bogus: they have no historic connection with pre-Christian paganism, and remarkably little interest in actual history as opposed to fabricated-from-whole-cloth fantasy.
I'm no expert, but that's as much as I (think I) know.
So yeah, they may have had miraculous wells or healing springs associated with the convent.
Okay. Thank you for the education, my FRiend.
There were a lot of different factors at work in this -
1. The "Enlightenment" distaste for revealed religion of any sort, thus any miracle must be pagan, not our nice rational Church of England.
2. The protestant distaste for Catholicism's local, physical associations and a desire to stamp out devotions to the saints as "a fond thing, vainly invented" led to a disavowal of the site of any miracle. This is why Walsingham, for example, was razed to the ground and the ancient statue of Our Lady formally burned in London.
3. The "cool" factor - pagans are SO much cooler than plain old ordinary Christians!
4. It sells, tourists eat it up. See No. 3.
5. Historical ignorance. Surprisingly prevalent.