RG59 is supposedly high loss cable, not recommended for a cable run of any length. I used it one time because I had a lot, but have since got rid of that for all Rg-6 cable. I did run some 59 under the house from a splitter to another tv, and am about to throw that, soon as it is warm enough to make me want to tackle the crawl-space lol.
I had a functional second birdview dish that was originally used for audio feeds only, so pq was not a big deal to me. I re-aimed that dish keeping it stationary on 137 West. It was fed by RG-59. Quality was not the best. Changed the cable to RG-6, immediate improvement. You may find a better overall system with the upgrade of the cable. Small price to pay for big improvement in your system's potential.
It is still ok for things like analog video cameras and other applications that use relatively low frequencies (think VHF, FM radio, etc). If I was replacing or installing new cable it would definitely be RG-6 or better. Comparatively small price difference and RG-6 can be used pretty much anywhere RG-59 was used but offer much more flexibility for the future.
I always use RG-6. However, if you are using something that is working, such as RG-59 in this case, if it ain't broke then don't fix it. No point in fixing something that is still working. It also don't hurt to upgrade it to RG-6 though. I have seen RG-59 being used and later it would burn out and require a cable replacement.