Probably impossible to say as nobody can forsee our future space traffic, but at some point it will get more difficult, as the risk of getting hit from tiny bits of metal that fly with an insane speed will get higher and higher when leaving orbit.

This debris is dangerous to our astronauts and satellites already, so maybe instead of thinking of year XY when we can't travel anymore, think of a rising chart. The more shit we shoot in space, no matter for what purpose, the quicker the line on the chart will grow and the more risky it will get.