Buy it for Life

BIFL and Bluetooth are typically an impossible combo because Bluetooth means more batteries and electronics to break/be unreplaceable. Maybe modular systems will come in the future but they'd need to use a completely generic set of batteries.

My best suggestion, based on what you describe as your problem with wired headphones, is to get headphones with a removable cable, as those cables are generally pretty standard. I know sennheiser had a lock in mechanism but you can get third party cables. Also, I was able to take that out of my HD599s and use the headphones with a Bose cable.

Fairphone make headphones, slightly over your budget but worth a look. I've had mine for two months and they've been solid performers so far. More importantly, Fairphone places an emphasis on ethically-sourced and easily-repairable products with a long lifespan. Their new phone comes with at least eight years of support, for example.

Edit: alternatively, find a decent pair of dumb headphones with a detachable cables, either USB-C or 3.5mm, so you're less likely to damage the cable and, if you do, you don't need to replace the 'phones.

I like the AKG brand, I got 3 AKG headphones over the last 2 decades. One of them was stolen, one was gifted to my father after changing the pads and I still have the 3rd one.

They are lasting well and sound amazing.

The K371 might be close to what you are looking for, it's wired but comes with multiple detachable cables and it's a standard mini XLR so even if it break you can easily replace it.

Audio-Technica ATH-M50X for all around use including mixing. They are Bluetooth but will also support analog cable in case Bluetooth goes away as a supported format.

For gaming you just can't go wrong with the granddaddy of them all. The Astro A40 with MixAmp Pro. Try the A50 if it has to be wireless but note that it won't be BIFL.

I'm 2 months late and you probably already bought something. But in case anyone else with a similar request to OP is looking through these comments, I recommend Souncore life q30s.

They have good audio quality for the price (approx $60-80), and can connect with both Bluetooth and replaceable headphone jack wire. So if the Bluetooth components or batteries break, you can still use them as wired headphones.

The only con I found is that they skimped out on the mic quality to make the audio quality higher and maintain that price point.

My Bose QC35 is starting to give me intermittent issues connecting Bluetooth. I've also changed the foams 3 times. I've had it since 2016, using frequently. I don't think it gets much better than this.

Lots of suggestions here already but if you want something truly BIFL then unfortunately Bluetooth is out of the question - look at things that have replaceable cables instead (such as the Philips Fidelio 2XHRs). Alternatively, for something actually rugged, maybe look into used genuine 3M Peltor Comtacs - the audio quality is surprisingly good for what they are.

Shokz aren’t quite over the ear in the sense that you are thinking as they are bone conduction. But they are definitely put on and forget. I don’t know about buy it for life but they apparently have great customer service. I’ve had mine for about 4 years now I think and I love them. My friend had his for quite a few years and then something went wrong with the audio quality so he called up the company and they just sent him a new pair with zero hassle. He’s now definitely a customer for life. I think you would probably need to buy new for that kind of customer service though.