Help me not screw up my Vampire/Human Romance

When writing a human/vampire romance, during a plot in which the vampire is struggling with their bloodlust, what are the potential cardinal sins I should be trying to avoid if I want readers to want these characters to stay together?

(If there's any situation-specific information that might help, please ask.)

Well, there's tropes and cliches about vampires, and then there's tropes and cliches about romance. Tropes and cliches aren't inherently bad in-and-of-themselves, but how you handle them really impacts whether or not your readers will go "ugh that is so cliche" or enjoy the familiarity.

Without knowing any details about your story, I'd recommend avoiding glamorizing or romanticizing abusive behaviors, which is going to be difficult because a lot of romance tropes and cliches do exactly that.

Like, it's one thing to have the vampire force themselves onto their human partner to feed because of bloodlust; it's another thing entirely to wave away that violation as being unintentional and continue to present the relationship as a desirable or ideal one (which is what a lot of vampire fiction does). There should be serious consequences to the relationship should the vampire succeed in actually feeding, and there should be serious consequences should the vampire come close feeding, and really, there should be serious consequences for the vampire having the bloodlust, period.

Now, those consequences don't have to be relationship-shattering, but they do need to be present, and they need to be followed through (which a lot of vampire fiction does not do).

Basically, the struggles the characters go through to maintain a relationship despite the bloodlust should be treated as serious and have lasting impact upon the relationship, even after the bloodlust becomes a non-issue (if it ever does). Giving the human partner greater agency is also a good idea, because that way the relationship is more on an equal footing, rather than the super sexy dangerous vampire overpowering the weak human lover (which is a trope I would love to see done justice considering the symbolism vampires have long held in Gothic literature, but which far too often isn't).

Having both partners actively involved in finding a solution to dealing with the bloodlust would probably be my main suggestion, mainly because doing so will help you naturally avoid a lot of the cardinal sins of vampire romance.

It'll also make the story different from most other vampire romances, which could be a good thing if you're aiming to write something a bit different.

Thanks for that feedback, it's exactly what I wanted. Now here's some details regarding this particular situation, if you'd be so kind as to tell me if you think it'll work as the sort of relationship I want to present.

So up to this point, they've been on very equal footing and are always on the same page. The 'vampires are sexier' trope isn't really present, and they fall in love just because their personalities are so compatible.
When the vampire's bloodlust becomes a problem (there's an in-story reason why it wasn't an issue until now) there's a scene in which the human is bleeding and the vampire finds it hard to control herself, and is struggling to prevent herself from going into a feral state over it. She comes dangerously close to losing control.
This scene is presented as scary, and she comes off as downright unattractive. We see that the human is understandably terrified.
She leaves the situation and he approaches her later when they've both had time to calm down.

She's rather torn up about what she could have done, and expresses shame and regret. She asks the human if he still wants to continue with the relationship, when she fears the possibility of this happening again.
He consents, though he is also still afraid.

The vampire consults other, more experienced vampires for advice and is reassured that one can learn to control their bloodlust over time if they're dedicated enough.

The vampire decides to try to learn to control her bloodlust, but leave the human if that plan fails and it looks like he might be in too much danger.

As for the consequences of the bloodlust scene, interactions are really awkward between them for a while after. The human is trying to be open and supportive, but he involuntarily flinches when she enters the room and she can tell that he is still afraid. The vampire is trying to be kind and friendly, but going into an almost feral state over your boyfriend’s blood isn’t something you live down so soon, if ever.

So seeing as she makes sure they're on the same page about continuing the relationship at all, I feel better about this to some degree.
I'm just hoping this will be enough.

It will ultimately come down to the execution in the end (because sometimes things slip in unintentionally that work against your intentions in writing the story; see Twilight for an excellent example), but what you've laid out sounds really promising. You'll probably be fine, though I'd recommend finding someone who can beta the story and point out any unintentional thematic/situational sabotage.

Just based on what you've shared though, I'd be very interested in reading it. I'm too busy to beta right now, but your story sounds really interesting, and if you post it up on here, let me know so I can take a look.