My iPod classic won't sync since I got iTunes Match. Any suggestions?

What happens when you try? If you are getting an error message, what does it say?

Also, select the iPod in iTunes (click its device button on horizontal bar) to show its settings screen in iTunes window. Along the left side (in the sidebar), under Settings, click Music. The iPod's Music settings screen is shown to the right. The checkbox for Sync Music turns ON automatic syncing. Is it currently checked?

NOTE: If it's not currently checked and you checkmark it, any songs on the iPod that are not in your iTunes library will be lost.

Checkmark Sync Music, if it's not already. Below that, if your iTunes music library can fit on your iPod, you can choose the option to sync Entire music library. Then click Apply.

One iPod classic DOES work one of your two playlists? But the other iPod classic does NOT work with the other playlist?

Does the iPod (the one that does not sync) appear in iTunes when connected? Since this problem occurred, have you done a Restore on the iPod, to erase it and give it a fresh start?

Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support

That makes more sense... The reason both of your iPods do not sync with your current iTunes library is because your current iTunes library is not the same iTunes library that previously synced with your iPods. It's a new (different) iTunes library to the iPods (even if it has the same content as the old iTunes library). iPods can only be associated with one iTunes library at a time, using automatic syncing.

When you associate an iPod with your new iTunes library, its existing content is replaced with content from the new iTunes library. Whether you do a Restore or not, the iPod gets "reloaded." It may take a while to sync, but not THAT long. My iTunes music library is about 50GB, and it takes about two hours to do a complete sync with my (older) iPods.

So, it's up you, but here's how to do it, without doing a Restore. If you do a Restore, you also do the same thing after the Restore completes. Select the iPod in iTunes (click its device button on horizontal bar) to show its settings screen in iTunes window. Along the left side (in the sidebar), under Settings, click Music. To the right, the iPod's Music settings screen is shown.

NOTE: You offloaded all songs from iPod, but for anyone else reading this, any songs on the iPod that are not in your iTunes library will be lost.

Checkmark the box for Sync Music. This turns ON automatic syncing and associates the iPod to the current iTunes library. Below that, choose the option to sync Selected playlists, artists, albums, and genres. Below that, under Playlists, find and select (checkmark) one of those two mega playlists. Then click Apply to sync the songs on that playlist. Repeat same steps for the other iPod, selecting the other mega playlist.

Going forward, iTunes keeps the iPods "in sync" with changes your make to those two playlists in your iTunes library, the next time you connect each iPod (or click Sync if already connected).

To avoid this situation in the future, you should back up your iTunes data to an external drive. This document describes one way to do it.

Manage and back up your iTunes media library - Apple Support

If you back up your complete iTunes folder, when restore it (from backup) to a new computer, it is the same iTunes library (not a new one with the same content). Your iPods will treat the restored in iTunes library as the same iTunes library (because it is), even though it's now on a new computer.

See Recover your iTunes library from your iPod or iOS device for content on the devices that isn't in your library or elsewhere.

See Backup your iTunes for Windows library with SyncToy for a strategy to backup, or restore that backup to a new computer.

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