For me, recordings (regardless of how well-written a song it is at the core, aside from the arrangement) sound dated for two reasons:
1) It's an arrangement driven song, where the arrangement has taken an OK tune, but in the hands of the right producer with good musicians, the chart really dresses things up and makes it stronger than it actually is. Arrangements, and the production styles and recording methods, change over time and can sound dated years down the road in light of what's current. Phil Collins had made some wonderful, timeless records, but on the other hand, what the hell is going on under 'SuSudio', and that song is a big zero without whatever all that burbling mess underneath it.
2) The instrument tones (which can be part of the production process, obviously. . . .) can be dead giveaways. The big slap echoes on 50's records. The 'chikki-chikki-wah-wah' rhythm guitar parts in 70's funk. Disco's 'beee-oooooooo' syndrums, or the big gated snares or Simmons drum tones on 80's records, or the depressing detuned sound of grunge in the 90'. Lots of examples. Can definitely be part of the charm of some recordings, but instantly dates them, if you're old enough (like me . . . . ) to have heard the progression over time, you remember when these sounds were the deal.
Strong, great songs, with arrangements that don't cover them up, and timeless instrumentation recorded well escape this mostly. Smartly administered quality is timeless. Owen Bradley's Patsy Cline recordings, so many Jazz records, George Martin's best work with the Beatles, and others would be hard to be improved upon.
One of my favorite recordings is Orleans' 'Still the One'. I've heard this a million times, yet I can never imagine where I'd change one thing to 'improve' it or 'update' it. Any time I find that feeling, it never does nor ever will sound old.