Yes, Dr. Manhattan has the potential and perhaps inevitable descent toward entropy all things must ultimately embrace. He will either succumb to natural forces which may erode his abilities or psychological dissolution as he becomes more inhuman over time, thereby destroying the very humanity which allowed him to transcend death and gain his powers in the first place.
Jon Osterman a.k.a. Dr. Manhattan is a form of living consciousness bound together by the accident which subtracted his "intrinsic field".
His superhuman abilities are as vast as any seen in the comic genre and he is able to manipulate the fundamental aspects of the Universe itself.
Ultimately his powers are bounded by his mind and I believe he can and will at some point in the future/present/past (from his perspective) dissolve himself to become one with the Universe.
Making the Case
Dr. Manhattan is the only character in the Watchmen series to explicitly possess superhuman abilities. Throughout Watchmen, he is shown to be immensely powerful and seemingly invulnerable to all harm; even when his body is disintegrated, he can reconstruct it from atoms (in less than a minute the second time this happened). Jon has complete awareness of and control over atomic and subatomic particles. He can alter his body's size, coloration, density, and strength. He does not need food, water, or air, and is, for all intents and purposes, immortal. He can teleport himself and others over great (even interplanetary and perhaps intergalactic) distances.
His only apparent limits are the physical origins of his previously existing organically-derived mind. He still thinks like a Human because he was once human. As he developed in the use of his powers, his connection to humanity became more tenuous.
He would alter his size to be able to reach a component, or split himself into multiple beings to work at more than one place at the same time. These events would slowly erode his humanity, showing him just how far from the Human experience he has come.
His Only Limitation
A clear limit to his physical powers is never explicitly shown, however perhaps his biggest limitation appears to be apathy. In some sense, unlimited power has come at the cost of the total absence of responsibility, and his phenomenical omnipotence is juxtaposed with his growing detachment. Although he doesn't age in the biological sense, his character has changed over time with gradual detachment from humanity.
Adding to his potential for psychological imbalance, is his non-linear perception of time, being able to see the past, present and future simultaneously. This knowledge is both imperfect and able to be altered by his or others actions. This perspective further disconnects him from his Human experience.
His treatment of his fellow humans is ever more disconnected, as he makes no effort to ease the difficulties of teleportation or forgetting that Laurie can't breathe once he teleports them to Mars.
It is this psychological distance from his humanity will ultimately be the event that causes him to cease to exist, because it was his humanity that caused him to return to life in the first place!
Judging from his overall descent from concerned scientist to cold analytical being of cosmic power I would say it is likely an inevitable state he will find himself in where he will simply have no interest in a universe that is both completely deterministic and able to be completely understood and manipulated by him.
- Or he will make a determination to return to a complete state of oneness with the Universe and return his consciousness back to part of the Universal field. To him, it is the logical extension of the phrase "matter (or energy) is neither created or destroyed, it is merely transformed." From his perspective, once you can do all that there is to do, what is left TO do?
At the end of Watchmen we are lead to believe he will return to Earth for a time to watch the thermodynamic miracle that is Humanity. But I wonder how long will such a thing be able to hold the attention of a man who can be in multiple places at the same time, living in the past, present and future, while study both the microscopic and macroscopic physically, standing on both atoms and stars?