I never got the whole problem with Roxie's gym. People knew at that point that this Ash wasn't at the skill level of his Sinnoh self. Maybe a Johto comparison is more appropriate. I mean look at his battle with Clair for example. If he used his whole Johto team, he would have needed 6 Pokémon to beat Clair. If he called in Snorlax and Charizard for Roxie, he could have won with 3 Pokémon but he didn't. I know this was a problem for people because this is Gen 5 and Clair was Gen 2 but we knew when Ash was going for badge 8 that his skill level wasn't what it was in Sinnoh.
The problem is that its extremely bad writing and against Ash's character for him to accept those terms.
He'd want a proper battle and win and he'd know needing double the Pokemon to win (and even then barely) means he is weaker then Roxie. He refused Wattson's badge because Pikachu was supercharged, then only accepted it because Wattson admitted he was the cause of Pokachu being super charged, just like he refused the gift badge from Volkner and demanded a proper battle with Skyla. Ash wants to win his badges fairly, not be given freebies (that was just Kanto, since Johto he earned them all properly). A properly written Ash would have refused the badge and say he'll beat her 3v3 next time and given him a rematch after the Junior Tournament.
Just like it made no sense based on Ash's character that he never challenged Marlon and Drayden.
Well, it was already established he wasn't as good as he was in AG and DP since there was a reset so considering his reset, he didn't do horribly against Roxie. He probably would have needed 6 of his Kanto Pokémon to beat 3 of Giovanni's Pokémon and 6 of his Johto Pokémon to beat Clair so I think 8th gyms are tougher in general.
Him being "reset" makes absolutely no sense, especially considering he's called back Charizard and Dawn showed up. Meaning its pretty clear older saga's still happened and he still has all prior knowledge.
Making him suddenly forget how to battle (like has match with Cameron) nothing more then very poor writing
And yes, he did horribly against Roxie, barely winning with double the Pokemon means he did a very bad job, especially considering she is literally the weakest gym leader in B&W2 (Cheren might be first, but he intentionally uses a weak team), he had 3 Pokemon who got owned and Pikachu and Pignite got to shine again. Thats the same problem as the league. The writers give Pikachu, Pignite and Krookodile all the wins and reduce the remaining 7 Pokemon to fall guys who lose horribly and often quickly.
He was a rookie back in Kanto and Johto (even then Pidgeotto beat Giovanni's Rhydon and Pikachu beat the rest, just because Jesse was using them didn't make them suddenly weaker), so his team being weak by Gym 8 wasn't weird back then since he was still a rookie, but he should know how to fight and train his Pokemon properly by now since he's an experienced veteran at this point, he did so in AG and DP, yet suddenly forgets in BW and reverts back to rookie (including losing badly multiple times to a rookie who just got his first snivy).
In AG he had a proper team of 6 powerful Pokemon by the end, most evolved or at least powerhouses and in DP he had 2 fully evolved starters by the end along with multiple powerhouses
In Unova he started out strong, capturing a lot and evolving a lot, showing improvements and so on, then Roxie showed up and basically owned him (Koffing took down his toughest and then his fastest Pokemon with little effort) and after that except for Krookodile nothing happened to his team, he didn't improve, he didn't learn anything and then we got the worst league ever written in which Ash seemed even less skilled then back in Kanto followed by multiple plots with Team Plasma that didn't even need Ash in them and now he's drifting from island to island with no goal whatsoever while we basically wait for XY.
Written properly and based on the knowledge and experience Ash should have destroyed Trip in every battle, have properly trained and evolved team, beaten Roxie with in a 3v3, fought Drayden, beaten Marlon, destroyed Cameron and won the first Don Battle and Junior Cup. He failed at all these because the writers lowered his skill level for plot purposes or to make others shine.