While in combat the quickslot tab of your inventory will reset to the top of your inventory list at irregular intervals, making it extremely difficult to change a quickslot item while a member of your group is in combat. This is especially prevalent in cyrodil, where you might encounter this bug trying to add recently purchased siege equipment to your quickslot bar in a keep which is already being attacked.
Workaround:
Your regular inventory does not suffer from this issue, so you can drag an item from that inventory to the quickslot tab/button, and then to the quickslot wheel.
Speculation:
The interval at which the quickslot tab resets is extremely irregular, as such I suspect that it is something which a group member is doing, such as taking or doing damage from/to an enemy player, perhaps firing siege of their own.
This bug has existed since 2014, I vaguely remember encountering it on a beta weekend, but I my memory may be playing tricks on me.
Eternal Destiny (PC/NA)
Dead Wait (PC/NA Haderus AD)