It’s well known that “Febuary” is a common pronunciation (and spelling – 706 million hits on Google, but with multiple warnings about “Did you mean to search for February?”), but it’s by no means the only English word that tends to lose an r or /r/. Usually it occurs when two /r/ phonemes start consecutive syllables: arbitrary, contrary, deteriorate, library, literary, as well as February, but there are cases where a syllable intervenes between the two /r/s: secretary, veterinary.
After February, secretary must be the word in which this phenonemon caused the most complaints at my time at the BBC, when any perceived ‘dropped’ /r/ would bring letters on to my desk. And yet veterinary is accepted without question by almost everybody when it is pronounced /ˈvet(ɪ)n(ə)ri/. No one ever complained about it in my 23 years of answering such letters.
What I notice is that if the two /r/s are in adjacent syllables, it is the second that is dropped (e.g. deteriorate > ‘deteriate’), whereas if there is a greater distance between them, the first one disappears (‘Febuary’, ‘secketary’, ‘vetinary’). In the case of meteorological, either the /r/ or the first /l/ can go, but more often it is the /r/, leaving /miːtiəˈlɒdʒɪkəl/ – rather than */miːtiəˈrɒdʒɪkəl/.
I don’t know of an explanation for this, but perhaps someone else can supply one.