Why did Robert Reichel bounce between the NHL and Europe multiple times? That's easy: money. During the 94-95 lockout he played in Germany, and though he came back to play for the Flames after the lockout ended he was like a completely different player. He gave up on defensive play pretty much entirely, and looked slow and totally disinterested in being there. After finishing his contract he was an RFA and refused to sign the entire 95-96 season. He went back to Germany instead.
The Flames did eventually sign a new three-year deal with him in 1996, but he was a shadow of the player he was three years earlier. He didn't even last a year with the Flames: they shipped him out to Long Island before the 96-97 season's end. All of a sudden not being in Calgary turned him back into a >1 point-per-game player again; thereafter he became one of my all-time least-favourite Calgary Flames players. It was like a switch was thrown, and he magically started giving a damn again.
It didn't last long. He played another 1.75 seasons in New York before they tired of him too, and sent him packing to Phoenix. This was the last year of his deal originally signed with the Flames, and just like when the Flames sent him to the Islanders he became a PPG player again when he went to Phoenix. After the Coyotes blew a 3-1 series lead against the Blues I think he felt unfairly maligned in the press, and admittedly it wasn't all his fault (Jeremy Roenick got hurt in game 1 and they sorely missed him), but him and his agent stuck it to Coyotes GM Bobby Smith and adamantly refused to sign a new deal in the offseason.
By Mid-August 1999 the negotiations were so acrimonious that Bobby Smith publicly announced that Robert Reichel would never, ever play another game for the Phoenix Coyotes, and when pressed about what he'd told Reichel's agent Paul Krause, he said: "I told him to lose my [phone] number."
So Reichel went back to Europe, again, this time his childhood home in the Czech Republic to play for hometown team Litvinov. It took Bobby Smith two years to get rid of his playing rights, trading him to the Maple Leafs in the summer of 2001.
The Leafs gave him the money he wanted, and he dutifully played out his three-year contract, but he was on the wrong side of 30 and Toronto fans and media excoriated him in his first postseason for pulling a disappearing act: no goals in 18 games. He played 37 playoff games for the Leafs in three seasons, and cumulatively scored two goals. (Both of which came in 2003.) Not what you need out of your second-line centre.
By '03-'04 he was made effectively redundant by the Leafs acquiring former Flame teammate Joe Nieuwendyk, and had no NHL contract when the '04-'05 lockout began. He went back to Litvinov and never came back to the NHL; too many bridges burned.