What are best practices to get verified on twitter?

Did you get denied? Or have you not been approved *yet*?

I'm not sure how Twitter is working through the application process, but from what I can tell it is roughly in order based on follower account with a big focus on who they are and how much their name or personal brand are attached to why people follow them.

Congrats on growing your following! Twitter recently changed their requirements and made it somewhat easier to get verified. However, I've seen where people have to apply as many as five times before Twitter finally approves them for verified status. Make sure you are really focused on having your profile look extremely legitimate and keep applying every 30 days!

As far as losing followers, if you're using a tool like Tweepi or ManageFlitter and unfollowing people, it's possible they are utilizing a similar tool and will pretty quickly unfollow you as well. Really can't think of any other reason for that to be happening, quite an anomaly. Keep an eye out for trends and start making notations to see if you can further decipher why you're randomly experiencing a drop off. Twitter Analytics might be worth looking into as well.

I'm a verified twitter user. I hope my advice helps!
What do you mean when you say you engage? There are many ways to do this, and how you use it will influence how they see your activity on the platform.
You should reach out to people in your niche and retweet and contact them, and do so in a way that is almost never about promoting your brand (that would be spammy).
But even if you are the best twitter user around, ultimately the purpose of verification is because you have some form of celebrity, where people imitating you is a genuine concern. So if you have come across accounts that claim to be you, or websites that use your face (a problem I was facing), then that is important to use, as the whole point is that the tick mark shows that you are the real you compared to any potential fakers.
For the question of losing followers, that's troubling, and even if you never paid for them if they are leaving in those amounts it may also be a case where your account is randomly followed by fake accounts to make them seem real and other people will pay them to get a follow (so they don't exist to follow one accont, which would be more suspicious). If twitter sees that a lot of people are unfollowing you, even if it's not your fault, then that will hurt your chances. You may want to contact their support separately to their verification department and see what's going on there and solve that problem first and foremost.
If you have further questions about maintaining authority online, which will help the verification process immensely, feel free to give me a call!