I'm thinking of English in particular, but any information about any Germanic language is welcome as well!
Dutch and Swedish have also lost the distinction between masculine and feminine, instead combining them into a "common" gender, whilst neuter nouns remain as a separate gender. In Swedish "dialects", you still encounter it as a separate gender to some degree, like in Norwegian, as well as occassionally declining adjectives before masculine persons with an -e instead of -a. Den svenske mannen, but den svenska boken.
In Dutch until the 1940s, they wrote in a highly artificial and archaic style, which intentionally brought back the distinction between masculine and feminine nouns, although they used German and Latin examples for assigning gender, showing that the process of losing the distinction already happened in the "dialects" by the 1600s when this style started since they didn't resort to local less literary forms to help.
Now in English, it's after the great shock of the Norman conquests that we see both a collapse in cases and genders, although in the works of Chaucer, the Pearl Poet and so on, into the 14th century, we still have remnants, the final e was pronounced when written (different from today's silent e, which is generally not actually silent, rather instead changing the pronunciation of a preceding vowel not and note, rat and rate), but there was no distinction in gender. So it was lost in the intermediary period, between 1066 and 1150.
*1150 The change in English wasn't over night for the general populace, at least I wouldn't expect it to be so extreme, although already in the Peterborough Chronicle by 1154 at latest do we note a lack of gender (using the/þe for all nouns!), besides in pronouns, at least in writing, indicating either a "declining" standard of English among the literary classes, using Norman French instead of a change through out the entire populace, although I'm not to knowledgeable of the historical backdrop in the time, but I find the shift to be extremely quick. Another possibility would be that the Old English documents we have were extremely conservative and that gender had already started to be lost before the Norman Conquest, but only with the loss of literary education in English was that shedded in writing. I'd need to look into the Ormulum more, as it could display a distinction still, it seems a lot more conservative than the (few) other English texts from the period, which could however mean that that was how the populace was still speaking at the time.