I tried to persuade X to go, but I couldn't.
I came across someone writing a sentence ending in a contraction, similar to the one above, and someone else saying that it's uncommon, and that "but I could not" would be better. Is that the case?
I know that contractions shouldn't be used in formal writing, but that's not what I'm asking about. There's a similar question on English Language & Usage, but I'm not sure that nohat's answer is what all English language learners would like to read.
Ending a sentence with a contraction is entirely valid in normal English.
I tried to force myself to eat the last bite of cheesecake, but I just couldn't.
Oh, go on. I'll eat this whole chocolate bar, even though I know I shouldn't.
No, really. I mustn't.
Really. Don't do it. Just don't.
Put a spider in her bed when she's sleeping? You wouldn't!
You two are going out, be we aren't.
Your ice-cream is tasty, but this one isn't.
You want to go to the mall? Yes, let's!
I can't remember sending that email, but I must've.
I didn't do it, but I could've.
The time now is eight o'clock.
How may I help you ma'am?
Greets, y'all! (warning: not standard English)
In fact, in the above, use of the non-contracted forms instead of the contracted-forms sounds stilted, although your point will still get across.
Note that there are some contractions where, as Bill points out in the comments below, one would not normally make use of them at the end of a sentence:
She's not going home for Christmas but I am (not I'm).
She's not going home for Christmas but we are (not we're).
You hadn't eaten a chocolate pudding, but I had (not I'd)
That experiment isn't awesome this project is (not project's)
That idea won't work, but this will (not this'll).
OP is already aware that using contractions isn't always appropriate (in formal writing, for example), so the only issue here is grammatical constraints on the use of contractions at the end of a sentence.
In general, you can contract not to n't at the end of a sentence, but you can't contract a verb form except if it's an auxiliary verb associated with an immediately-preceding "primary" verb.
Per discussion on wordreference.com, #3 here is a practical example of that exception:
1: John hasn't won the lottery, but I've. NO
2: John hasn't won the lottery but I have. OKAY
3: John didn't win the lottery, but he could've. OKAY
...where in #1 and #2 the verb have can be seen as an "auxiliary" form - but since it's not modifying another verb immediately before it (such as could in #3), it can't be contracted.
I haven't been able to find any authoritative source covering this particular issue, so the "rule of thumb" as given is simply my own phrasing to cover all valid/invalid examples I can think of. If anyone knows of a usage that doesn't fit my rule, please post it in a comment, rather than silently downvoting the answer.
