When is pretty easy. During the classical period the improvisation became less common. When you look at a standard Baroque piece, say a Bach flute sonata, you see a ton of repeats. The convention was to play it once as written, and then to play it again with ornamentation as the player sees fit. In most Baroque sheet music published today, you will see a lot of the ornaments and cadenzas written out, with younger players performing it as written, and more experienced players (hopefully) using the written ornaments as a guide, and making up their own as they go. A lot of this is simply Baroque performance practice, like figured bass which also lost favour during the classical period. A part of the reason why this declined is the reason why it existed in the first place: flexibility.

Say you're Bach, and you're asked to write a flute sonata. The accompaniment may be a harpsichord, or an organ, or a Viol, or any other possible continuo instrument (if you're not a musician and need an explanation for any of these terms, please let me know). So, as a result, you'd have to write an accompaniment that could be played by any of these instruments, hence figured bass, which just uses numbers to denote chords, and allows the continuo player to make up an accompaniment based around that chord structure.

Same with ornamentation. Castrati schools, for example, practiced ornamentation and trills for hours every day, and would embellish a song with all the fancy, difficult, and impressive ornamentation that they could handle, and show off their virtuosity to the best of their ability. However, if one guy can trill an F6 for 10 seconds, that doesn't mean the next guy can, and he may just do a lengthy, fast coloratura cadenza, because that's what he's good at. Likewise with instrumentation; you don't always know what you're getting. There are examples in the Baroque period of this, such as Boccherini's sonatas for Flute OR Violin, or Bach's Sonata for Flute OR Recorder and the like, which is something you would never see today.

In the Baroque era, you would never know what instrumentation you would have available, as some people had some musicians on staff, but not necessarily an oboe player, or a flute player, or they wouldn't necessarily have access to a harpsichord, so the more versatile your compositions were, the more likely they would be to be played more often.

As you move into the classical era, you start to see music get larger. More symphonic works and less chamber works, and instrumentation would be more fixed, and composers didn't have to be as flexible, and could write something that could only be played by a Violin and Piano without too much worry that there would be no violin and piano available. So you could push the boundaries a little more in your compositions, and add cool things like double stops, or spiccato in your composition without having to worry that a flute, oboe, or recorder wouldn't be able to perform it. Again, not that composers didn't have those options in the Baroque era, but when you're balancing the desire to write something cool, with your desire to make the most money possible, some people are going to err on the side of money.

So composers can write more fixed pieces, push a little further, and write the piece they want the performer to perform, while taking some of the artistic license away from the performer.

That sounded rambly. Does that make sense to you?

As our resident flutist already commented, Baroque practice was very improvisatory, and things started to change in the Classical. The size of the ensembles is a very important factor: it's not so easy for 30+ people to improvise, it's much more manageable with 2-6.

The emphasis in structure is also very important. Baroque composers were frequently creating a platform for musicians to build upon. Classical composers started to work more on terms of doing the actual development of the material a priori. It's not easy to develop musical material on the spot, and it gets harder if you want to create a structure that is big in terms of time (5 minutes of coordinated development between n musicians). Planning that thing and writing it down is much more doable.

Structure became a very important thing for art in that period (especially in the German world), and that tendency kept going well into the 19th century (we could argue it's still doing very well in classical music). In the 19th century we see a lot of support for formalism.

Formalism suggests that the meaning and beauty of a work of art is entirely determined by its form. That is, by its intrinsic order, by the relationship between its constituent elements. This is contrast to previous ideas. During the Baroque, there was this idea that music can literally affect your state of mind because it can move the configuration of the humours in your body (yes, seriously). Music was great because of the details in the way text was sung and things like that.

But if you think music is only great because of its structure, then you do what you can to create great structure. And improvisation makes it more difficult to accomplish.