If a character is pinned with suppressive fire during combat, rolls willpower to shake it off and gets a success. The rules says "he may act as normal the next turn". This means he cannot longer be pinned or I can do it again?

I think it can be pinned down again the next turn if the enemy shoot a suppressive fire again, since it would be a new action.

Pinning RAW is too strong I would houserule it starting with removing the -20 modifier and giving situational modifiers.

Thats said its best to do sth. like that before you start a campaign or at least discuss it with affected players to come to a mutual solution else players can feel "betrayed".

You can indeed pin someone down the next turn. And again, and again. The thing to note is whether they're still subject to the suppressing fire action - a perfectly natural (indeed, to a degree mandatory) effect is to dive for cover. If a target is in full cover and not in your line of fire, they're no longer a target for the next suppressive fire burst; as an extreme example, a target inside a closed rockcrete bunker which is not in line of sight and not in danger of being hit under any circumstances cannot logically be affected by the burst, even if within the 'firing angle' - indeed, they might not even know you're there....

Obviously, they'd then have to spend a half action moving back into your line of fire (standing up from prone, or whatever) but they won't be pinned.