At What Point is the Needle Damaging Records?

I have used my Denon 110 between 1-5 hours a day for the past three and a half years, and lately I noticed the highs are beginning to sound a little muted. Could I damage my records by not replacing the cartridge right away?
It's time to replace your cartridge.
The needle is always damaging the records.
You should repoace the Stylus.
You could have the cartridge retipped. but it may cost more to do that than it is worth.
Get a new cartridge.
You are a little overdue, the damage might've been done already, hopefuly not.
Of course, the needle always damages records but let's not take this subject to the extreme.
Have you examined the stylus with a loop or magnifying glass. Perhaps you simply need to adjust VTF/VTA. I have my catridge (Transfiguration Temper W) more than 5 years and listen nearly as often as you do and highs are as sparkling as when I first installed it.
It may not be stylus wear but rather the suspension giving way. I don't know how to check that, but I agree with Stew, check the VTF/VTA first.
Get a loupe or magnifier and carefully examine the stylus. Sometimes you'll find dirt is the issue. A layer of grunge may have built up that does not come off with normal light brushing.

It may be difficult for an untrained eye to spot mild wear, but it's still a pretty good habit to visually check the stylus periodically.
Ask yourself which is less expensive, replacing your cartridge or replacing your record collection. I think you know the answer. You asked if you might damage your records by not replacing the cartridge now. You described the sound you are beginning to hear. Do you really need a second opinion?
That's about $00.09 a day, not bad. Buy a new cartridge.
That's quite a few hours, I agree you may need a replacement. As mentioned check your set-up and try this cheap method to clean it;
According to Neil Young, he's seen the needle and the damage done, a little part of it in everyone. :-)

I would replace or retip it.
Ballpark is 1000 hours I believe. Your way over that average. It probably will be different with every setup. Tracking distortion happens in a lot of cases. Sometimes, it will show up more in the inner most track. It has been said if you have damaged grooves from one shape of stylus, using a different type of stylus shape may still sound ok as it will ride higher or lower that the damaged part of the grooves.
I thought a typical stylus lasts about 2000 hours and it usually outlasts the suspension. Is this not the case?
I thought a typical stylus lasts about 2000 hours and it usually outlasts the suspension. Is this not case?

I could be wrong as I'm going by long term memory. I looked around the net, and Shure says about 1000 hours, and people were saying 500 hours or more on VinylEngine. I think some times they used to have timers that went to 999 hours from what I can remember. They're aren't all the dealers like we had in the vinyl only days, that used to have a good microscope to check to see how it actually was worn. I wonder were those good microscopes went? They might be in storage somewhere being wasted, or in someones collections that knew better than myself. Links to what I found.
Pardon my grammar.

Have you tried demagnetizing your cartridge before assuming stylus damage?
Here are a couple of links to those old stylus microscopes some dealers had in the 70s. Mcintosh dealers had to buy a lot of gear back then. The Wild Heerbrug was $4000 back then. That's about $17,000 in today's dollars. Audio Classics said theirs cost them $6800 dollars. I can't find what the Shure microscope cost back then. Links.[] []
Sorry, try Shure link again. http://www.shure@global_managed/documents/webcontent/us_pro_sek-2_ug.pdf
I guess their system doesn't like it.[] If you want, copy and paste might work if this doesn't.
I'm sorry. Google "Shure phono cartridge microscope". The SEK-2 is one of them. C/PEK-3 the other.
Stylus microscopes - while it's always nice to have a specially designed, dedicated professional tool for a job, it's a classic mistake to assume that having nothing is the only option if you can't have the fancy one.

Some magnification is better than none. I've got a little 8X printer's loupe that lets me see all kinds of things I can't with the naked eye and I doubt it cost $15.

Same story with sound level meters. Depending on the specific abilities, calibrated meters start at hundreds of dollars and quickly go much higher. Yet the $50 Radio Shack model can be extremely useful to the home listener.