Especially for motorcycles? I remember back in the 70’s nearly all engines had the camshaft inside the the cylinder block and used push rods and rocker arms to move the overhead valves. Overhead cams were mainly a racing modification. Now OHC come as a standard feature. How much more durable is a motorcycle engine that uses push rod OHV compared with one that uses OHC?
Short answer: not really. OHC bikes include things like Goldwings so there’s obviously no inherent longevity shortcomings. The only major manufacturer that sells pushrod bikes in any great numbers in the US is Harley and that’s mostly for aesthetic reasons, not any particular engineering one.
Now, if you happen to be in the market for a new sub-$1000 bike somewhere in the developing world, pushrods may have an advantage. Those sorts of cheap bikes are going to be knockoffs of old designs from the major manufacturers, and pushrod designs are going to a bit more forgiving of poor materials and sloppy tolerances than an OHC one. There’s definitely a reason why knockoffs of the old Honda Super Cub OHV engine dominate the ultra-cheap motorcycle market.
I see. Well, if you could keep it a secret from the other Dopers, I’m learning to ride rather late in life and my starter is a 125 cc honda push rod. Not a fan of those noisy underbones with DOHC and six-gear transmissions. 
OHC engines almost always are designed to rev higher then pushrod engines.
Higher revs will result in more heat energy, and greater wear on parts. This could be designed out by increasing surface areas of bearing surfaces, increasing lubricant flow, improving the cooling system, along with some materials changes. You will also need a mechanism to drive the head cam, which is also subject to design requirements.
You are also more likely to look at having more valves per cylinder to aid the engine revving. Whilst you are doing that you will also probably increase compression ratios, which in turn requires a closer examination of how to secure the head from escaping higher pressure gases.
You will then have a trade off over the physical size of parts, and on a bike that will be important.
There is also the trade off of costs.
A push rod engine will usually be cheaper to manufacture.
All the above being said, engine design has moved on dramatically since the '70’s where top ends of engines were often the limiting factor in the life of a motor cycle.
These days bikes can expect realistically to go well over 100k miles without a top end rebuild - and you could not have really said that 40 years ago.
Well, however many tens of millions of people have bought small-displacement Honda pushrod motorcycles (or their derivatives) can’t be all wrong! I’ve got an early 80’s vintage 110cc one in my fleet that does what it does very nicely.
Apart from the manufacturing issues, pushrod engines do make a bit more sense in lower powered bikes because low-end power is much more important. For faster bikes, the major power needs are at the high end with overcoming wind resistance at highway speeds. Even relatively modest bikes capable of highway riding end up having ridiculous power-to-weight ratios, so low end grunt is not an issue. But squeezing out every last HP at the high end is, so OHC engines are a no-brainer. Smaller bikes behave more like a car, though, in that they need a pretty big proportion of their power to overcome the weight of the vehicle and rider to get rolling. So a pushrod motor isn’t a terrible choice there.
Overhead cams reduce the mass and inertia and number of bits involved in moving the valves, so they work well at higher RPM which increases the specific horsepower. One or two cams will suffice for an inline engine design.
Long stroke engines with poor balance can’t really rev anyway. In a Vee or opposed engine, it takes one or two cams per cylinder, so it adds a lot of expense/complication. Also makes the engine taller in the case of a Vee, so it isn’t the Harley way.
The longevity of all but Chinese motorcycle engines will exceed the use a typical rider puts it to. 50K miles is a very high mileage motorcycle. Yes, there are touring riders who do lots more. But they represent a fraction of 1% of the motorcycles out there. Far more bikes rust into unusability (or get wrapped up with a car or tree) with barely 10K on the clock.
Said another way, the OPs Honda has more longevity than he needs. And the limiting factor is going to be some nuance point of that particular engine model’s design, not some high level architectural factor like pushrod vs. OHC.