Harry wanted out. He has been alive for too long, even by wizard standards, and so he had been testing his supposed "Immortality".
Harry doesn't truly believe himself Immortal, because he knows that every thing will meet an end. What that end is, he doesn't know. Stars, Galaxies, Black Holes, all of these will succumb to Death's grip. Harry believed that Death's personification [dubbed 'Derek' by Harry] will meet an end. His reason for thinking this is the simple reasoning of "What reason is there to have death if there is no life?"
At least, Harry knows that Death will die in this plane when there is no more life. Derek dropped enough hints that even the oblivious Harry Potter was smart enough to put together that there are other "universes". Harry wouldn't ever get a straight answer out of Derek if there is, though, he figured that Derek couldn't unless Harry force him to, and Harry would never force his friends to do something they don't want to do or against their will.
Point is, Harry has been, in the eyes of the mortals, been attempting suicide for a long time. He has made friends with other mortal races, or at least quasi-immortal races. They seemed to understand his want for an end, as within their races they are still able to die, hence the 'quasi' part. Even a phoenix at one point decides to stop being reborn, or a ghost to 'pass on'.
Harry had no real enemies, or at least his 'enemies' don't want to kill him. Harry found it ironic that his friends want him to finally die, but his enemies want him to live.
Any real enemies, if he gets any, don't last long. At least, to him it isn't long. People quickly catch on that it isn't a good idea to make enemies with a suicidal immortal being.
For a couple hundred years Harry had joined a military, namely the Human military, and he was giving the suicidal mission. Often he went alone. At one point the opponent managed to capture him, for a brief time, and Harry decided to do something completely 'Suicidal' for even most quasi-immortal beings. He thought it was a good idea to blow up the reactors powering the ship he was in, blowing apart the ship, and spitting him out at warp speed. It took a while for him to be able to slow down to an acceptable speed so he could go back. Harry thought it was fun and an educational experience.
Harry retired from the military service, which was unsurprisingly easy. To anyone else he didn't actually even exist during the time he worked for the government. Later he found out that the reason the military decided to make his retirement as painless as possible was because they were afraid of him. Apparently their fear of what he can do overridden their want of having him within their folds. Rightly so, as he could basically cripple the galaxy's economy and put them into another Depression with the wealth he amassed over the years. Basically, he could buy the government and the ones in the know, knew the kind of missions he successfully completed and walked away from, without anyone really knowing it was him.
For the next few thousand years Harry existed, occasionally taking contracts from within the gov. of the time, and doing whatever caught his fancy.
At the end of that brief vacation period, Harry was talking with Derek. "I know you've hinted at there being other Universes, or 'Planes of Existence', could you possibly place me in one of them? I'm kind of tiring of this one.'
Derek looked at Harry for a long while before he (it?) said, "I cannot, nor any other being [primordial or otherwise] tamper with your current state of being. That includes your placement." At seeing Harry's downtrodden look he quickly continued, "But, that does not mean you cannot change you cannot."
Harry immediately brightened at the news, and it made Derek smile to see Harry happy. To anyone [or thing] else, it would have been the scariest thing they ever would witness. harry, however, always did like Derek's smile. It always made Harry feel good to know that he can bring a smile to his normally stoic friend.
On a side note, it always made his immortals friends [that were in the know about him and Derek] confused to hear he is a friend of Death. They thought that Death would despise those that cheat him, and becoming immortal is cheating Death. That's not necessarily true, it is only if you come back from death that it is cheating him as that is going against Death's judgement. If you are 'immortal', he needn't worry, because you didn't die yet.