Statistical models for environmental monitoring strongly rely on automatic data acquisition systems that use various physical sensors. Often, sensor readings are missing for extended periods of time, while model outputs need to be continuously available in real time. With a case study in solar-radiation nowcasting, we investigate how to deal with massively missing data (around 50% of the time some data are unavailable) in such situations. Our goal is to analyze characteristics of missing data and recommend a strategy for deploying regression models which would be robust to missing data in situations where data are massively missing. We are after one model that performs well at all times, with and without data gaps. Due to the need to provide instantaneous outputs with minimum energy consumption for computing in the data streaming setting, we dismiss computationally demanding data imputation methods and resort to a mean replacement, accompanied with a robust regression model. We use an established strategy for assessing different regression models and for determining how many missing sensor readings can be tolerated before model outputs become obsolete. We experimentally analyze the accuracies and robustness to missing data of seven linear regression models. We recommend using the regularized PCA regression with our established guideline in training regression models, which themselves are robust to missing data.