I thought the longbow became less popular due to the time and effort of training archers, especially as (1) guns became more common, and (2) the post-plague heyday of successful, well fed, empowered peasants with spare time began to wane.
This article says that longbows were less effective as plate armor became more common. While the chronology generally matches up, I thought plate armor was reserved for the ultra-rich. Were there enough knights on the field (and/or did regular soldiers have access good enough armor) that the longbow's efficacy was meaningfully diminished?
https://m.warhistoryonline.com/medieval/longbow-rise-dominance.html
Firstly, plate armour was not reserved for the ultra-rich. In the 16th century, cheap munition armours (like this one) could cost under 12 shillings (not cheap - still a month's wages for a craftsman). For a relevant past discussion of the prices of armour by u/WARitter see https://www.reddit.com/r/AskHistorians/comments/5ebcwm/during_the_15th16th_centuries_how_was_the_process/
Secondly, armour other than plate will protect against longbows (and crossbows), if sufficiently thick. Mail, especially in a sandwich of textile-mail-textile, will stop arrows. Brigandine will stop arrows. The transition to munition plate for the common soldier was driven by (a) plate having become cheaper than mail (and brigandine) for the same protection, and (b) plate providing better protection against firearms.
It isn't so much a case of longbows becoming less effective because plate armour became more common, but longbows becoming less effective because armour became more common. A good example can be seen in battles between England and Scotland. E.g., at Dupplin Moor (1332), English archery was very effective, since the Scots were poorly armoured (still, the Scottish attack reached the English lines despite heavy archery), while at Flodden (1513), English archery was largely ineffective since the front ranks of the Scottish infantry were well armoured.
Thirdly, even if armour is common in the enemy army, archery is still useful since
even if breastplates would stop arrrows, limb armour was typically thinner and could be penetrated,
armour has gaps,
even if many soldiers are armoured, not all soldiers are armoured, and
horse are often unarmoured even when soldiers are armoured.
However, when armour is common in the enemy army, guns are potentially much more useful than archery.
I wrote this post a while back discussing the decline of the longbow in england during the 16th century, though it focuses more on the role that guns played rather than armor. u/Hergrim, u/MI13, and u/WARitter might be able to go into more detail about the effect longbows had on armor or the effect that armor had on longbow archery and there was a pretty fascinating discussion on arrows vs armor here.
Armor wasn't really the key factor in the longbow's decline however given that the longbow continued to see use well after the use of armor in europe seems to peak in the late 15th-early 16th century. Accounts from the battle of Flodden in 1513 do claim that the scots were well armored enough that the english archers did little damage, but at the battle of the Spurs that same year English longbowmen were still said to have played a significant role in routing the French cavalry. The Mary Rose, famous for its large number of well-preserved english warbows didn't sink until 1545.
In 1591, when the debate over abandoning the longbow completely was getting extremely heated, Sir Roger Williams estimated from his experience that perhaps as few as 1 in 10 infantry would actually be well-armored. Even with armor taken out of the picture however, muskets or arquebuses still had a lot of advantages which made them much more useful than a bow in skirmishes or siege warfare.
English sources in the late 16th century generally do consider the longbow's usefulness primarily limited to shooting at unarmored men and horses, but I suspect that this was more of a "compared to guns" thing rather than an indication that armor had improved greatly since the 15th century. English soldiers continued to use the longbow in Ireland a bit longer than they did in the low countries since the Irish were still considered poorly equipped in both armor and firearms. Even this doesn't seem to have lasted too long however before, according to Barnabe Rich in A Martial Conference:
. . . our barbarous Irishmen, that invented targets made of small wickers, like basket liddes, which weighing not above two pownd weight, would cover them from the toppe to the toe, and sometimes with their mantles hanging loose about their armes, whiich was the cause that our captains of that country, long sithence have converted all their bows to calivers, and from that time have so continued.
