No, according to the Adventurers League rules
I asked a similar question on the Adventurers League Dungeon Masters Facebook group, and the consensus seemed that when a magical object has hit points and receives enough damage to get to 0 HP, it is destroyed and looses its magic forever, without possibility to repair it. Here is a relevant extract from the AL FAQ (emphasis mine) :
Shatterspike can't be used to destroy magic items, unless the item itself specifically provides an AC, hit points, etc. in its description. In that case, it's hella good at destroying them. Take that, magic net!
Here, we can see that the AL FAQ hints that magic nets can be destroyed, not only broken. It continues :
Unless the conditions of an item's destruction is specifically stated (talon card from deck of many things, ioun stone, +1 nets, etc.) permanent magic items can't be destroyed, Items destroyed in such a manner follow the normal rules for intentional or unintentional destruction.
We can determine that a net's destruction clause (AC 10, 5 HP) is intentional, and so the AL guidance states :
Some items have conditions that include the ability or potential to intentionally destroy the item. If destroyed, these items still count.
So, to summarize : a magical net that gets destroyed by having its HP reduced to 0 will lose its magic, and if repaired, will simply be a plain non-magical net. However, the magical net will still count towards the wielder's Magic Item Count.
Still citing the AL rules, you could argue that a destroyed magic item is not necessarily rendered nonmagical, because of the following text :
Permanent Effects : Some items are destroyed or rendered nonmagical when used, [...]
If so, you could then say that a destroyed magic item could be repaired and keep its magic. I think there's AL rules preventing that, but not quite sure at the moment (edit needed).