MATLAB graphics underwent a major upgrade a few releases back, so it's hard to know exactly what your figure looks like without knowing what release you're on, or better yet seeing an example and a clear description of what you are trying to get. So I'm not sure what problem you are running into. As Adam says, I think maybe the root cause is that you have a bunch of small plots, with not enough room to properly label the time axis.
If you have access to R2016b, this makes a pretty nice plot of your data, see attached:
time = datetime(1979,1:432,1);
y = randn(432,27);
tt = array2timetable(y,'RowTimes',time)
ttplot(tt)
ttplot is on the File Exchange. If you're using something between R2014b and R2016a, you can still do that using a table (rather than a timetable), it's just not quite as immediate.
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