Hiding line when data point intervals change

I might not be finding an answer to this question because I'm not thinking of the right way to search it, but here we go...

I have a simple temperature vs time for a greenhouse monitor. Occasionally something happens and either my program crashes, internet goes down, whatever, but I don't gather a data point, maybe for a couple hours to a couple days. I normally gather a data point every 3 minutes if it's up and running right. The plot is a line, and it will connect the line as a straight line to where the data starts up again. I want it to break the line if data isn't gathered for... say... 30 minutes (10 missed data points). Is there a way to do this?

Thanks!