It is an awesome idea to do this. Twitter moves in real time, if your followers aren't watching the first time, maybe they will see your tweet the second or third time.

No you can repost same tweet it does not seems to any problem.

it is absolutely fine to repost tweets multiple times.

Personally, If I am one of your subscribers I won't like to see the same tweet again, and again. I would like to see different tweets. If you page is really established, it may work, but otherwise I think its best to use new ones every time.

Its fine to repost posts especially top performing posts.
Alternatively, you can try "string" your tweets together: String Together Tweets. Increase Twitter Engagement!

It is a good idea.
Repeat Your Tweets Multiple Times. Not everyone is online all the time so make sure that your best Tweets are seen by your followers.

I would space it out if you are gonna repost the same content. Wait a couple months then repost it again saying if you missed out on this here it is again.

I post my web contents again and again. Like 5-6 times a day. The posts change when there is a new post.

Twitter users do not use twitter the whole day. Some will use it at 5'o'clock, some at 6, some at 8 and so on, so a person will not see the same post again and again. Instead, the user at a different time will have a chance to read your post.

Do not repost too much though. Around 4 to 5 times should be OK.

Even news channels and TV episodes re telecast all the time

I never tweet the same thing twice because I have another method... I have 2 accounts & both have over 10k followers so what I do is retweet & then un-retweet so I can tweet again.

I call it juggling tweets. If however I only had one account I would make my tweet then after a few days delete it then post it again... my twitter approach is appearing to keep tweets to a minimum when actually posting as much as possible.

I also keep a strict ratio: Have more followers than what you are following & make less tweets than the amount of followers you have (this only applies after you get going because initial tactics are different)