it should last for a good, long while as long as you don't abuse the system. it's pretty much just like anything else. I've been sporting a jtag for about 10 years now. it's never failed me. I think most of the 360 models shouldn't give you much trouble, unless it's a xenon. steer clear of that.
Its “technically” a modchip style installation. Goes down to, how good the install was, capacitors over time etc.
Mine is in a air tight sealed bag. Been there for about 2 years now. I only got mine back out to help someone with Aurora the other month and to finally copy the rest of content I had left to copy over, the HDD, since it is moving, could die before the console. However, SSD are CHEAP now. Eventually I will upgrade my Trinity to an SSD for preservation.
While there have been people suffering dodgy lasers or drives dying most of the problems were RROD motherboard failures, and the DVD did not exacerbate that really (it is not like the DVD drives draw all the power and introduce all the heat). Most of those are limited to the earliest 360 models, though for practical purposes if it is an original style 360 and not a Jasper most consider it a more when than if for RROD with the earlier models being both older and more prone to it in general.
So yeah clean the dust out, don't shove it in the back of a cabinet with no air flow and chances are you will be sitting pretty for as long as any other piece of hardware like that will last. If and when it does kick the bucket then emulation will probably be the better choice anyway, or maybe there will even be drop in replacement boards.
tbh it sounds like either you did something wrong with the original xboxes or the modder didn't do a very good job, i had a modded original xbox and it lasted until i stuck it away in the loft (it probably would've lasted longer, but i think it got thrown out at some point).
unless you mean a modded original xbox 360, many of the original xbox 360 models had a terrible build quality especially the Xenon models, back when the JTAG mod was first released so many people botched already dead 360 consoles back to life so they could perform the JTAG hack and sell them at a premium, there were inevitably going to die again in a very short amount of time but with the original JTAG hack being limited to low dash version consoles there was an abundance of dead consoles that hadn't been online for a long time sitting in peoples closets