Gohan's profile:
真面目で知性派! パンのパパだ!!
悟空とチチの間に生まれた。真面目かっ理性的な性格で、子供の頃からの夢だった学者になっている。悟空譲りの力は健在で、ピンチの時にはサイヤ人パワーを発揮する!
Serious and intelligent! He's Pan's papa!!
Born between Goku and Chichi. He has a serious, rational personality and has dreamed of becoming a scholar since he was a child. The power inherited from Goku is still alive and well, and in times of crisis, he can demonstrate Saiyan power!
Goten's profile:
ノリ は 軽いけど 父親讓り の パワー の持ち主!
悟空ファミリーの次男。子供の頃は悟空そっくりだったが、今ではすっかり都会派の青年に成長。お嬢様・パレスちゃんに夢中のあまり、最近ではめっきり修行不足らしい!?
Although he has a frivolous attitude, he inherited his father's power!
The second son of the Goku family. When he was a child, he looked exactly like Goku, but now he has grown into a city-oriented young man. He's so obsessed with his young lady, Palace-chan, that he seems to be lacking in training lately!?
This book seems to suggest that Gohan stayed in shape and kept training ("[his] power inherited from Goku is still alive and well"), whereas it explicitly states that Goten stopped training ("he seems to be lacking in training lately"). The
Perfect Files ("he hasn’t neglected his training") and Vegeta's line in episode 2 (in which he implies Gohan hasn't been slacking off from training like Goten and Trunks have) also backs up the notion that Gohan kept training.
However, this same book contains the following statement from Atsushi Maekawa:
English translation of the Atsushi Maekawa Story Q&A from the 2006 Dragon Ball GT Dragon Box DVD release in Japan
www.kanzenshuu.com
For instance, in Gohan’s case, there was apparently so much as an “Ultimate Gohan” concept in Dragon Ball Z, where he was a super-warrior with might surpassing Goku, but in GT, he’s a scholar who’s given up fighting almost entirely.
Gohan training is probably treated separately from him fighting; most likely, he kept up his training despite not fighting during the 15 years of peace following Boo's defeat. Maekawa later says, "around the time of the Super Seventeen arc, [Gohan] suddenly returned as a super-warrior". In actuality, Gohan started fighting again during the Baby arc and his role in the Super Seventeen arc wasn't any different. So, "he returned as a super-warrior" just means "he started fighting again". However, although Gohan may have kept training in GT, Maekawa's comment suggests that he's no longer Mystic, as he speaks about the form in the past tense.
Overall, I think he kept training enough to stay in shape and not be any weaker than he was in the Boo arc, but not enough to be anywhere near Goku, who rigorously kept training in the 15 years that had passed since then. As for whether or not he kept Mystic, I believe he lost access to the form itself due to not training quite enough, but can still access the same amount of power by transforming into a Super Saiyan (logically, SS2, but that form is basically non-existent in GT). This is only my speculation, though. Toei probably just made him turn Super Saiyan because they felt it looked cooler without caring about the logic behind it. GT's a mess.
(Weirdly, Trunks isn't said to have stopped training in his profile):
冷静沈着な頭脳派ファイターだ!
ベジータの格闘センスとブルマの頭脳を受け継いだ、超エリート戦士。カプセルコーポレーションの社長業に忙しい毎日だったが、べジータの命令でドラゴンボール探しに出る!
A levelheaded, intelligent fighter!
A super-elite warrior who inherited Vegeta's fighting sense and Bulma's brainpower. He was busy with his duties as the president of Capsule Corporation, but at Vegeta's orders, he set out to find the Dragon Balls!