Training irregular time series data

[jpf18]

I am wondering if Chronos can effectively be trained on irregular time series data. This is data that is captured in minute intervals during the daytime, with no data available overnight. Conceptually, in production, a trained model would be used to predict a 45 minute window from a 45 minutes long context beginning every morning. Side note: This is a single statistic, so breaking up each day into individual items does not seem to be the way to go.
I've experimented with training data in one piece, where the resampling step infills rows in the requested minute interval, leading to a 60%+ infill rate as a result of the missing overnight data. When training using this approach, the resulting models do not converge to provide effective production predictions (as one would expect). So the question: Is there a way to structure such irregular data and train Chronos to achieve effective model fits?