I agree with Dash8driver.
If You have the required visual cues at the point where You lose the GS, continuing visually may be the best option.
If You are still in IMC, it depends a bit. Continuing on a LOC approach needs to have been briefed; the minimum bug must be reset, the diverse fixes (FAF, stepdowns and MAP) must be known to the flight crew. Of course, in theory it is allowed under most OM-As to downgrade the approach before having passed the outer marker, but this comes at an increased workload and is not always a suitable option. If either of the flight crew holds the slightest doubt about continuing, then going around and properly preparing the next approach instead of allowing one to be rushed into an ad-hoc NPA is the better choice by far.