I currently have 3 Fairies that I got from a Great Fairy Fountain. However, I've since opened up two other Great Fairy Fountains and neither of those had fairies around them. I've been playing quite a while and I haven't had them respawn at the first great Fairy Fountain either.
Fairies will only respawn if you have less than 3 Fairies.
The number of Fairies that respawn at each Fountain are as follows:
Fairies Left : Fairies at Fountain
3+ : 0
2 : 1
1 : 2
0 : 3
So, release all three fairies and 3 Fairies will spawn at each Fountain, which will allow you to have up to 12 Fairies at once.
Fairies can only spawn if you have less than 3 fairies in your inventory.
Fairy fountains always spawn 4 fairies, though it takes some time until a fairy that you caught, or that flew away, can spawn again.
Since the game only counts the fairies in your inventory it is possible to hold some in your hand, in order to reduce the amount of fairies in your inventory to under 3, to make more fairies spawn and get considerably more.