Does an "escape velocity" exist in this situation (see details)

Here is the scenario: There is an almost completely empty universe. It does not have to be completely empty, but any other mass/energy must be small enough that it has not effect on how events play out. In the universe, there is one planet and one spaceship on the planet. When the spaceship is launched, it instantly accelerates to any given velocity and then stops acceleration forever.

Here is the question: How would one calculate the minimum possible velocity that the spaceship needs to be able into space forever, without ever coming to a halt?

Here’s the catch: Since the gravity of the planet is felt everywhere in the universe, the spaceship always experiences the forever-decreasing but never zero effect of the planets gravity. The spaceship is always slowing down, but always less and less as time goes by. Does an escape velocity exist in the first place?