Very similar to my experience with an Eversolo A6ME (Jims), and an A8, followed by my A10 - all sounded just ho-hum when new. A6 flat/lifeless for several days: A8 took about a week before it started to ‘sing’, but my A10 took well over a Month before it settled in and the SQ became stable (I could hear it improve almost every day).
My (just received yesterday) Denafrips Pontus 15th sounded just like you said, quite flat with ‘soft’ sounding bass and midrange, with a ‘zing’ to the top end. It’s been running non stop now for 24hrs, and I’m just about to try it on familiar stuff.
Did you know that Denafrips say (on their website) that all their kit is burned in for 100 hours before shipping Tristan?
That would mean those massive differences you heard actually happened between 100 and 150 hours of use…
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As mentioned above, valves get worse as they near their life span expectancy. Also Elecro caps have a short, relatively, lifespan. Some larger caps have just a 2000hr lifespan, when used at their max temp rating. So. Class A amps with large reservour caps have to use caps rated at 85°c or even the 105°c versions, which get very expensive. Apparently, with each reduction of 10°c under the rated temp, the lifespan increases by a factor of three.
Yes Jim, and it also means that it may still be getting better for many hours use after that.
Dom, there’s one company who believes that cable burn in is a real thing, and, wait for it, wait for it; he even claims that if you take the cable out of circuit, then put it back in, then you must go through the whole burn in process all over again!!!
‘As mentioned above’
@Stu got 90% of it right in the second post - psychoacoustic habituation.
The rest of it is caps, especially electrolytics. Anyone specifying component values who has an eye to longevity will ensure there’s abundant margins overhead in terms of voltage rating, ripple current and thermal characteristics - otherwise you potentially doom your company to dealing with more returns-for-repair than is healthy for your reputation, especially as circuits age. Not a consideration in lower-margin electronics (almost everything else), where saving £0.00001 means the bare minimum spec is de rigeur.
Electrolytics require a few cycles of charge/discharge to ‘form’ - i.e. reach optimum performance, and this goes from ‘a few’ to a ‘a lot’ if you’re operating them well below their anticipated design envelope. This will sound better with time, because until they are properly formed, they are not actually doing their job properly!
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Now you say, I do seem to remember that. I think I’ve seen photos of them being soak tested in the factory. Their burn in time is well reported on various knowledgeable audio forums 
.
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That’s the “burn-in” sorted. What about the “loot-in”?
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Rather narrow minded and unrealistic to think or expect a designer/manufacturer to have the space/time/facilities to power up what could be hundreds of components and keep them powered for what could be several weeks, especially as most people know that new electronics need a ‘break in’ period. And as most manufacturers don’t do that - do they all not know what they’re doing??
Hmmm. Where to start (again) ? Perhaps here
I’m going to stick my neck out and suggest that most people don’t know that. Ask a bunch of people who’ve just got themselves a new phone. Do most.of them know that it’ll not be at its best for a couple of weeks ? I’d bet my pension that they don’t.
I spent a few years being paid to worry about electronic control systems at the interface between state-of-the-art lasers and accelerator-based light sources. That included some time spent making real world systems work in very challenging electromagnetic environments, often under a deal of time pressure. Some of the kit was expensive (silicon-chip-filled boxes costing tens of thousands of pounds) and it could be a struggle to get it to deliver the very challenging performance that we’d paid for. In-person help by technical experts from the manufacturers wasn’t that unusual. But honestly, not one of them ever said "You know what, this phase noise analyser is brand spanking new. You need to leave it running for a couple of weeks. It’ll be all over the place until then. I’m getting back on the plane to Santa Clara CA and I’ll show up again when it’s had time to burn in. ". Really, that wasn’t A Thing.
As far as I know, when it comes to electronics audiophiles (and not even all of them) are the only people who believe that weeks of burn-in is necessary.
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No, no, no.
If that were true, then all the kit we buy that gives strong initial underwhelm would all have been a huge waste of time, effort and money. This obviously cannot be the case so the laws of physics and chemistry must accommodate.
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Can I do the Hamlet quote now? Can i? Can I? 
? Full fathom five, thy father lies?
Act1 Scene 5
There are more things in Heaven and Earth, Horatio, than are dreamt of in your philosophy.”
(Scientists eh! Think they know it all )
Or
There is nothing either good or bad but thinking makes it so.
Different year, different Shakespeare 
I would tentatively suggest that burn-in is the audiophile ear performing a slight flinch when confronted by a new piece of equipment in the system. Will it blow up? Sound awful? Etc. This flinch will increase the more expensive and exotic the piece is, hence a longer period of burn-in is required. Of course the quantum nanoparticles need to be fully aligned to hear anything at all.
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Indeed, we did A Midsummer Night’s Dream 
Oh christ, silly-season’s satrted early…