I didn't study Latin, but I can recognize when a noun is singular or plural.
It's weird that date is used in the singular form data in Portuguese - a Neo-Latin language - while Dutch contains the form I'd say makes more sense, datum.
Italian, Spanish, Portuguese (etc.) data, and French date (whence English date) are all taken from Mediaeval Latin data, the plural of classical Latin datum, but reinterpreted in these languages as a singular noun. German and Dutch use the classical singular form datum.
All of these are bookish borrowings from Mediaeval or Classical Latin (so-called cultisms) and not organic descendants of the Latin words.
There's probably no straight answer, why this happened in two languages. Here's just one hypothesis that may give a good start.
The etymology of "date" in English (and, likely, in other European languages) is:
The Roman convention of closing every article of correspondence by writing "given" and the day and month -- meaning perhaps "given to messenger" -- led to data becoming a term for "the time (and place) stated."
A Roman letter would include something along the lines of datum Romae pridie Kalendas Maias -- "given at Rome on the last day of April."
As we see, the assumed full sentence is something like:
"This message is given on [day, month, year, and place]."
"The message" is singular, hence, "datum".
It is easy to suppose that "this message" may at some languages/areas change its meaning slightly: "these statements are given…" or "these scripts are given…", both plural, hence, "data".
Since the difference is very slight, it can be supposed that singular/plural variants may cycle, even in the same areas.