Sure does. Most people who play regularly would be well advised to change strings several times a year, maybe every 2 months. You play more than most people, so you might benefit from changing strings more often. Once you change strings you should hear a nice difference, maybe a little too bright at first, but then a nice lively sound until the rust and dirt and little bends the frets put in the strings dull down the sound. You can always check that by running a finger underneath the string, along its length and see how smooth or uneven it feels. Especially under the 4th string, you'll feel the unevenness, due to the winding of the string being dented or breaking.
Besides sounding fresher, the banjo will also stay in tune better with new strings, as the overtones of old strings get a bit out of tune, causing the notes to never sound quite right.
Some people leave the strings on for long periods and enjoy the plunkier, less bright sound. I wouldn’t rule that out if you find you like that.
Another point: For people who pick hard, older strings are more likely to break, especially the first.
If you like the strings you have on the banjo now, take the instrument with you to a music store and have them measure the string gauges, and get some sets like that. If you want to experiment, try a light gauge and a medium gauge set and see how they feel and sound.
Good luck with your picking!