"capable of having a date affixed," 1837, from date (n.1) + -able.
Entries linking to datable
date n.1
early 14c., "a period or stretch of time, a season, an age;" mid-14c., "time when something happened or will happen," from Old French date (13c.) "date, day; time," from Medieval Latin data, noun use of fem. singular of Latin datus "given," past participle of dare "to give, grant, offer" (from PIE root *do- "to give").
From late 14c. as "the part of a writing or inscription which specifies when it was done." The sense transfer from "given" to "time" is via the Roman convention of closing every article of correspondence by writing "given" and the day and month — meaning perhaps "given to messenger" — which 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."
Out of date "no longer in vogue" is attested from c. 1600.
-able
common termination and word-forming element of English adjectives (typically based on verbs) and generally adding a notion of "capable of; allowed; worthy of; requiring; to be ______ed," sometimes "full of, causing," from French -able and directly from Latin -abilis. It is properly -ble, from Latin -bilis (the vowel being generally from the stem ending of the verb being suffixed), and it represents PIE *-tro-, a suffix used to form nouns of instrument, cognate with the second syllables of English rudder and saddle (n.).
A living element in English, used in new formations from either Latin or native words (readable, bearable) and also with nouns (objectionable, peaceable). Sometimes with an active signification (suitable, capable), sometimes of neutral signification (durable, conformable). It has become very elastic in meaning, as in a reliable witness, a playable foul ball, perishable goods. A 17c. writer has cadaverable "mortal."
To take a single example in detail, no-one but a competent philologist can tell whether reasonable comes from the verb or the noun reason, nor whether its original sense was that can be reasoned out, or that can reason, or that can be reasoned with, or that has reason, or that listens to reason, or that is consistent with reason; the ordinary man knows only that it can now mean any of these, & justifiably bases on these & similar facts a generous view of the termination's capabilities; credible meaning for him worthy of credence, why should not reliable & dependable mean worthy of reliance & dependence? [Fowler]
In Latin, -abilis and -ibilis depended on the inflectional vowel of the verb. Hence the variant form -ible in Old French, Spanish, English. In English, -able tends to be used with native (and other non-Latin) words, -ible with words of obvious Latin origin (but there are exceptions). The Latin suffix is not etymologically connected with able, but it long has been popularly associated with it, and this probably has contributed to its vigor as a living suffix.