Translation:That has been getting more serious every time.
Here's an link re: "each" vs "every".
Notice that "each time/every time" is placed at the beginning of the sentence in order to give emphasis to the repetitive quality of the situation.
I'm afraid you will discover that DL is very inconsistent about the demonstrative pronouns and adjectives. You can rely on the aquele/aquela/aquilo family meaning "that"; the este/esta/isto family should mean "this", BUT (just as in English "that" is not always pointing to something far away) it seems that, at least in Brazilian Pt, the esse/ essa/ isso family may be talking about something near by, or just mentioned and DL will set up "this" as the correct English. If you REPORT it they will put "that" into the computer, so that we don't get it wrong unfairly. Doing the translations you will see that the "esse" words often do leave an English speaker with "this" as the more natural, at other times they refer to something said some way back in the passage and then we would use "that".