If you are sending your essays as email attachments, it's likely the files you are sending are being rejected because the file names you are sending have "invalid" characters. For file names, it is best to stick to the regular alphabet or numbers, and if possible, use only eight characters or the "eight dot three" format like so: xxxxxxxx.xxx
Try to make sure you don't have more than one "." in the file name. Also make sure the three letter extension at the end is not exe, com, or dat. Stick with "doc" for the file extension if in Word, or "wpd" if it's a WordPerfect document.
It seems unlikely that the attachment itself would be rejected due to invalid characters unless your professor has requested the document in a particular format, such as Microsoft Word, and you are sending it in WordPerfect or from an Apple word processing application. Your essay might even be rejected if it's in a newer format than what the teacher can accept, in which case, if you are using Word, for instance, you should make sure when you save the file to use "Save As," and choose Microsoft Word version 6 which is more universally accepted. If you are using WordPerfect, you can also use Save As to save in "rtf" format, which might be accepted by a professor who uses Word.
If all else fails, copy and paste the text of your document into a Notepad text file and send it that way, with an explanation to your teacher that your properly formatted document was rejected by the email system. If none of these suggestions work, it might be your email system that's at fault, but that seems unlikely. Try rebooting and starting fresh.
One other possibility is that your essay file is "corrupt," meaning that although it seems to appear fine on your screen, other systems might have trouble with it. The easy way to fix a corrupt file is to open a fresh blank document, type the letter "X," and then insert your essay file into the "X file." Delete the X from the beginning of the page. Save the new file. You will probably lose a lot of the formatting, and may need to go back through the document to correct it, but you will have fewer problems with it in the long run.
I hope this helps. =)