Shows that got worse with age

[numberthirty]

Preacher

Each season literally made the season before it(in retrospect...) look like a masterpiece.

(Notable Very Tiny Exception For The Final Scene Of The Series...)

[Chris Lang]

Let's see... shows that got worse with age?

The Simpsons: Most people agree that the single-digit seasons were the best, though Season 9 had the infamous 'The Principal and the Pauper' episode which some see as a sign of the show's impending decline. For me, it's a toss-up between that episode and Maude Flanders' death in Season 11 (sandwiched in between two episodes involving jockey elves and laser-firing Teletubbies) as to when the show jumped the shark.

Xena: The first two seasons were excellent. But then things started to get a little awkward in the third and fourth seasons, and the balance between dark/melodramatic and silly and goofy was nowhere near as good. But the fifth season was where it became clear the creators were losing interest and wanted to move on, with all sorts of character derailments, characters acting stupid, and the end of the Greek gods with a truly ridiculous finale involving literal deus ex machina (Xena is given the power to kill the gods by the new monotheistic pseudo-Christian deity, and most of the gods die in truly ridiculous ways). I didn't even bother watching the sixth season.

Sliders: The first two seasons were fun trips to alternate worlds with alternate possibilities. The third season greatly dumbed things down to 'Monster of the Week' and movie knock-offs. Things got so bad John Rhys-Davies wanted out, and his character Professor Arturo was killed off. And the third season ended with a 'Dr. Moreau' knock-off where the recurring villain who killed Arturo anticlimactically falls off a cliff. From what I hear, things got worse from there, but I didn't bother sticking around.

Game of Thrones: Another case where the creators lost interest and just wanted to wrap things up. It started in Season 7 and got worse in Season 8, where a show that once took its time and gave story, characterization, and so forth room to breathe was suddenly rushing plot threads. Character actions suddenly seemed forced and inorganic, and even things that actually DID have some setup felt forced when the big payoff actually came because the payoff wasn't handled correctly. (See Daenerys' big turn in Season 8, Episode 5).

[DrNewGod]

Downton Abbey: as it progressed, it lost it's will to look at aristocracy critically.

[AndrewCrossett]

Xena: The first two seasons were excellent. But then things started to get a little awkward in the third and fourth seasons, and the balance between dark/melodramatic and silly and goofy was nowhere near as good. But the fifth season was where it became clear the creators were losing interest and wanted to move on, with all sorts of character derailments, characters acting stupid, and the end of the Greek gods with a truly ridiculous finale involving literal deus ex machina (Xena is given the power to kill the gods by the new monotheistic pseudo-Christian deity, and most of the gods die in truly ridiculous ways). I didn't even bother watching the sixth season.

Season five was an anomaly in that they brought in Kurtzman & Orci as showrunners. They had been in charge of the recently-ended Hercules series, which took a more broadly whimsical tone than Xena did. They didn't understand that Xena had established its own culture and tried to do the same things with it that they had done with Hercules. Didn't work, although I didn't HATE the season. It had its moments, and I looked at it as part of the whole.

Things changed significantly in the final 6th season, which many people think was the best of the seasons. (Except for the massively unpopular series finale.)

[Robotech Master]

Going with OP's definition of shows that got worse after a decent start, Sleepy Hollow. It had an excellent first season and first half of second, then suddenly every story thread rushes to a conclusion to set up a new baseline status quo, because there was pressure to minimize ongoing story threads and try to capitalize on the season 1 popularity by turning it into something new audiences could casually jump into.

But they had no good plans for an episodic narrative. So the show started to plod along, unsure of what to do with any element outside of its lead character's chemistry. Ultimately this led to said chemistry being undermined by the way so many other aspects of the world building and its characters were just ended one after the other like they didn't know what to do with them. One of the leads had enough and quit the show, and they thought they could reinvent the show and salvage it but despite best efforts couldn't do too much with what they had left.