As long as you avoid FD, the only character that can keep Luigi out forever is Villager (though a well-played Duck Hunt and Pac-Man can also be difficult to get in on). His mobility problems are exacerbated on FD, but on smaller stages it's not as big of an issue. Specifically, Halberd, Smashville, and especially Battlefield are great stages because they keep the fighting close.
Luigi's mobility is obviously his biggest weakness and as players looking to improve, develop his metagame, and ultimately win tournaments, we have to find ways to mitigate his weakness and play to his strengths. Personally, I've been trying to incorporate perfect pivoting into my game and PP -> utilt has been great. JC usmash is great too, and very useful when reversed. Bair has more range than I think you're giving it credit for and it can really put pressure on an opponent. Fireballs cover his approach, too. Crawling is something Luigi can do that I currently believe is underappreciated and underexplored. And of course, there's the classic approach of simply powershielding as you walk.
Luigi, like every other character, requires skill to get past his weakness in order to abuse his strengths. But damn, he is amazing once he gets in.