I think the answer depends on the situation.
- Space is big. There are millions of asteroids bigger than 1 km. We're not even close to having mapped them all, and they're not actively hiding. How do you tell a 100m ship radiating internal heat from a 1000m rock reflecting the sun? Spectroscopy, maybe.
- Sensors can be active like radar or passive like telescopes. The energy received with passive sensors scales with $\frac{1}{distance^{2}}$, the energy received with active sensors scales with $\frac{1}{distance^{4}}$. That means active sensors have to be really big.
- Passive sensors tend to have a very narrow field of vision. Not a problem if you're mapping natural objects, more of an issue if you look for a ship.
- It will be impossible to reduce the radiation from the ship to zero, and the background is not suitable for blending in.
- hard-science drives will use lots of energy, and radiate it freely.
That suggests to me it is very hard or impossible to break contact after initial detection, but making that initial detection is also very hard unless the ship radiates lots of energy towards the observer.