This seems like a big deal, to you, but really, it isn't.
That it is a longitudinal study means it's an even 'smaller' deal. Why? Well, because you've got months of data before the delay and months of data to come after the delay and your statistical analysis of your results will take care of the rest and fill the gap. If you don't know how to do this then you ask around and pick up the phone to someone who does. I spend all my time assessing longitudinal follow-ups and if you think that the follow ups all occur as intended then you are a dreamer!
Besides, have a some perspective - it's a PhD, not an intended Nobel prize. If the machine breaks down it's not your fault and as long as you show you did everything else correct then really, what's the problem? You just need to show you are competent and having a dodgy machine is no reflection on you. It's not worth losing sleep over.