This is one of those things I was hoping would be fixed after the ability delay patch. This affects everybody who binds their quickbar slots to mouse buttons.
The bug is this: If you bind any of your quickslot actions to mouse buttons (wheel up, wheel down, Mouse Button 3, Mouse Button 4, etc) AND your mouse is currently positioned so that it is hovering over your quickslot bar, then you cannot fire your abilities by pressing the corresponding mouse button.
You can verify this easily by going through the following repro steps:
1. Assign Quickslot 1 to Wheel Down.
2. Place your mouse cursor in the middle of the screen and move your wheel down, and notice the ability gets fired.
3. Place your mouse cursor on top of the quickslot bar but do not click any of the buttons.
4. While holding your mouse at this location, move the wheel down and notice the ability does not fire.
5. Move the mouse back to another location (away from the quickslot bar) and move the wheel down again, and notice the ability gets fired.
Because of the massive number of abilities present in SWTOR and the fact that I have a limited number of fingers / easily reachable keys on my keyboard, I often play like this:
1. Plan out an ability rotation that will span the next 0-30 seconds.
2. For those abilities which can be triggered with keyboard presses of keys that are very close together and I can move quickly from one key to the next, I use the key bindings.
3. At some point in the sequence, there will be an awkward key transition (e.g. going from pressing 1 to pressing Shift+7 or something). Since I've planned out my rotation in advance, I move the mouse cursor over the corresponding quickslot button in advance, so that when it is time to execute this action I can left click it immediately to fire the action.
4. After this happens, I cannot then immediately execute other actions via my mouse bindings, since my mouse will naturally be hovering over the quickslot.
Note that keyboard bindings are not affected by this bug, only mouse bindings. The obvious workaround for this is to move your mouse. However, I wanted to let people know about the cause of this annoying bug, as I know I can't possibly be the only one affected by it.
FWIW, I've already filed a /bug over this, and hopefully it will get fixed soon.