The main idea behind how the game determines if you fall down is an attack's Push Factor. This is what determines what you must do in order to stay up.

The second thing that decides whether you get knocked down or not is if you are moving. Depending on how you are moving, you become either easier or more difficult to knock down. There are 3 ways of staying up against an attack. First of all, you can simply stand still. Second, you walk directly into the attack. The way this works is that you counter the push factor of the attack with the forward momentum of your movement. The final way to stay up is by dashing into an attack.

Now here's a list of every attack these techniques would be used for.

Attacks you can stand still for
1st and 2nd combo hits from all characters
3rd combo hits from Obi/Ani and Vader
Obi/Ani's dash attack (only 1st OR 2nd part)
Luke's dash attack, 1st part only
Mace's dash attack

Attacks you must walk forward into
GG's dash attack
Mundi's dash attack
Luke's dash attack, 2nd part
Dooku's dash attack (1 hit)
Emperor's dash attack
Vader and Dooku stomp
Obi/Ani's dash attack (when BOTH parts hit you at the same time)

Attacks you must dash into
Vader's dash
Dooku's dash (both hits)

Attacks that are difficult/impossible to stay up against
3rd combo of GG, Aayla, Maul (standard 3rd and alternate), Mundi/Luke, Mace, Dooku, Emperor
Aayla's dash attack (must walk diagonally into, may not work against a good player)
Maul's dash attack (must walk diagonally into, may not work against a good player)

I will also show the mechanics of how backslash works here.

Backslash mechanics
The backslashes of Luke, Mundi, Obi/Ani, Mace, and Yoda have 2 hits, and both must hit a player standing still to knock them over.
The backslashes of Dooku, Emperor, and Vader also have 2 hits, again, both must hit a player standing still to knock them over.
The backslash of Maul only has one hit, any hit with Maul's backslash can knock someone over.
The backslash of Aayla has 2 hits, and both must hit someone standing still to knock them over. Not that this one has 2 sabers, one in front, one in back, so it covers 360 degrees better than others.

Now for how to antifall backslash. Unlike most attacks, backslash works by "pushing" you forward. In order to counter BS, you must walk backwards into it. This will counter the forward "push" of backslash. This works for all backslashes, including Maul's and Aayla's.

Another useful one that I've found is Aayla's saber lift at the end of her dash. It has the same properties as backslash. If you walk backwards into it, you will not fall down. Used correctly, you can backslash an Aayla in the middle of her saber lift and kill her. This is mostly useful with block on, as there are more efficient methods of killing an Aayla with block off.