I'll be honest, I have no sense of time after 16 years of drawing, but I've been told I work fast. So yes, I've improved over time by just... not stopping xD.
There are so many factors involved with speed though, from whether or not you're used to drawing the characters, how efficiently you use your art tools, and distractions in your workspace. There are 2 ways to get faster: Learn to draw faster and Eliminate wastes of time (distraction, switching between tasks too quickly as that slows you down, learn all the keyboard shortcuts).
My current rate is somewhere about 1-2 hours for a completely rendered complex panel. When batching together panels of 5 or more, the rate goes down because doing one stage at a time helps you focus in and avoid wasting time by switching tasks (going from sketch to line to color are three different modes of work, for example). So generally for story segment that 45 panels long, that'll take me 45 to 55 hours to complete. Working just 3ish hours a day cause I have 7 ongoing projects means one episode takes 15 - 18 days, so 3ish weeks.
I simplified the way I shade to save time too, an example of a Chapter title page:
Thumbnail (few minutes)
Pencils (I made two different sketches in fact so up to 30 minutes or so, fast and loose; by this point I had made a lot of concept art drawings of this character so i got used to drawing him and that speeds up the process too)
Inking (up to 30-40 minutes? I saved time by filling in darker areas for high contrast and depth+ save time shading; my favorite step)
Flats (Longest step but I did my linework on two layers, Outlines for major color sections on one and details on another so filling in flat colors is fast. that's another way to speed up flat coloring, but it takes some discipline with lines.)
Render (Shading and lighting, trying to stick to a bare minimum needed to add some depth to the coloring. using one shade hue per color area (but with a brush on opacity pressure so I can have sharp shadows within lighter general shadows) and gradient lighting over the whole thing for ambiance.)
Been drawing for 16 years self-taught
Been to college for art/animation -4 years of drawing and design-related classes
Been actually finishing comics only in the last few years, two one-shots and one premium comic.
My entire goal in college was to learn to draw fast and accurate. Drawing well and drawing fast are like a venn diagram with a number of factors that affect each side. You slow down to learn to draw well (learning anatomy, lighting, the theory), then you take what you learnt and practice doing it as fast as possible while gradually slowing it down in a session (About ten 10-to-30-second Gesture drawings, and five 1-minute , three 5-minute , and one 10-minute drawings is a classical way to practice)
There's a difference between training to get faster and just getting ambiently faster because the longer and more consistently you work, the more efficient you'll become just by that practice. The difference lies in the speed at which you can improve. IF you want to improve fast, then it requires training more often (like exercising for bigger muscles), and studying art. Otherwise, it's perfectly alright to just keep drawing, mindful of any improvements you can make through review and moving on to complete the next thing.
Combine that with eliminating distracting and time-wasting actions (those little 1-2 second things you do inbetween working adds up in the hours, days and weeks) and you're on a steady path to improve.