Can I re-apply if my application is rejected?
Yes you can re-apply. However, if you are re-applying then put as much effort as possible into addressing the reasons for failure. You need to show that there is new information being submitted with the second application which was not included in the first. A mere explanation in a cover letter will likely not suffice. The more documentary evidence that you submit which addresses the reasons for failure, the more of a chance that you will have to succeed on the second attempt.
For example, if you were rejected for financial reasons, then put new evidence addressing that particular reason into the second application which was not included in the first. This could include items such as bank account and investment statements, proof of ownership of assets such as real estate, letters from your employer, letters from guarantors, among others.
Unfortunately, it is a bit of an uphill battle with a second application because it is almost as if the default option on a second application is to reject. However, it is possible to succeed but some effort and thought need to be put into the precise reason for failure and how that may be addressed.