Will my iphone work forever?

If I were to use it for the rest of my life, would it work throughout those years or will it eventually die and never start working again?

No, eventually your phone will stop working. Battery problems, charging port problems, screen burnout. Thays not including water damage or dropping it or normal wear and tear.
The iphone however should considerably outlast most other phones with some tlc

Your iphone will work and after 50 years your grandsons will sell it has a antique piece…

If you manage not to drop it - either onto a hard surface or into any form of liquid, it'll live for about 3 years. After that time, you'll have to have the battery replaced (at the least). You'll have to repeat that procedure every (roughly) three years, as long as Apple (or whoever) makes these batteries available.

Next weak points are the digitizer (that part that recognizes your finger actions) and the LEDs for the screen lighting. I'd be surprised if they were designed with a lifetime much longer than the battery lifetime, although they might keep up for twice that time (depending on your usage of the phone - if they keep up with a heavy user for 3 years, they might work for a light user for 20 years).

I'm more tempted to say that your iPhone will not work for the rest of your life.

I say this because Apple hasn't made products like they used to. I still own an iPod first gen, and other than the fact that the operating system is outdated, it still runs as fast as it did when I first got it. On the other hand, I have nieces with iPod 3rd Gens and their iPods are already running slower than my first gen. I must also add that the design for the first gen is much better, in my honest opinion. I like the black metal frame and how it uniformly sits on the table.

vs

Keeping this in mind, I also own an iPhone 3GS which runs very slowly at this point and an iPhone 4S which is showing signs of slowing down. These signs are not too noticeable when it comes to browsing the internet; however, when I try to send longer texts 600+ characters, the typing becomes very laggy. Games also show occasional stop-frames due to lag, which they used to not.

Needless to say, it will probably become very, very slow to the point that it will frustrate you and you will throw it against a wall, break it, and then buy a new one and be happy and content again.

It will stop working as eventually it will old, out of fashion and out of date.