Старые привычки дают о себе знать, да?
I wonder if this is a commonly used expression to convey the idea of "Old habits die hard"? If an automatic translator is anything to go by, however, it doesn't seem to turn up any example of this phrasing.
In Russian, is it more like "Old habits are letting their presence be known / rearing their ugly heads"?
Yes, your translation is OK. Another one idiom (among translations you found) which is commonly used is
Привычка - вторая натура
The following is also often used, but has a little bit different meaning:
Горбатого могила исправит
This expression describes a person with negative qualities, who don't want to correct the behaviour. It could be applied to negative habits too.
There's another idiom which in some cases could be used to denote an unhealthy fixation on old habits or cravings:
Как волка ни корми, он всё в лес глядит.
Which roughly translates into "No matter how well you're gonna feed the wolf, he'll always keep glancing at the forest." or much more liberally, "You can take the wolf out of the forest, but you can't take the forest out of the wolf."
However, it will always have negative connotations and often imply relapsing into a former, inferior, state while neglecting other people's good will and attempts to change one's nature for the better.
Thus, it will be applicable to e.g. a paroled thug disillusioned with the hardships of an honest life and contemplating their return to crime, or to a struggling chain smoker whose significant other has been desperately trying to transition them to vaping to no avail, but it won't apply to a jogger who fractured their arm and had to take a break from their daily routine.
At any rate, it will almost certainly be perceived as something offensive if you tell that to someone straight out. Unless you both know each other well and you're confident that the recipient can take a joke!
There's also "старого коня [or пса] новым трюкам не научишь" (you can not teach an old horse/dog new tricks). Although it conveys a more pessimistic feeling of impossibility (e. g. they don't die hard - they don't die, period).
Волк каждый год линяет, да обычая не меняет.
English equivalent: The fox changes his skin but keeps his knavery.
Why just not say:
старые привычки не умирают
I think it's well used expression.
I also like this one, it can be used in this context: "Охота пуще неволи". It's not used as often, but it really should be.
