How long will your tzitzit last? That depends on both the tallit katan garment and the tzitzit.

I ordered a tallit Katan recently, and I’d like to order another soon, but out of curiosity I was wondering how long the usual lifespan of both the shirt and the tzitzit usually are if I wear it daily. Thanks!

A wool tallit katan usually lasts quite a while. Worn every day, I'd say six months or a year or more. It doesn't need much laundering, because wool doesn't absorb sweat and odors readily. The fringes in front might not hold up so well, but the rest of the beged should last.

A tallit katan garment made of cotton will not normally last as long, but is still likely to outlast the tzitzit strings.

Obviously if you are wearing the same tallit katan almost every day, even though it's protected under your shirt, it's still getting a lot of use. 

The tzitzit strings will inevitably start to look dingy after not too long. The question is at what point will the loss of whiteness start to bother you. Also, the tips might crimp and/or fray. You can snip off the tip (very little, say half a centimeter) several times, which will renew them significantly. See this post.

Thick tzitzit are likely to hold up a bit better than thin.

And if you have the initiative, you can certainly buy new strings periodically and tie them yourself. It's a fairly easy 30- to 60-minute job, depending on how nimble your fingers are.

How long the tzitzit strings hold up depends on a bit on the strings used, and a lot on the wearer. A six-year-old who's constantly sitting on the floor is likely to have fairly dirty tzitzit within a few weeks. At the other extreme, a man who wears a suit much of the day can expect his tzitzit to remain sparkly white for quite a while. Most people are somewhere in between.