3-4 a day isn't a big deal. It's a PITA to be sure, but doesn't really pose a monstrous security risk, that is to say, as long as the form and associated scripts can only be used to send email to your inboxes.
If the script that sends email from form can be hacked to send email to anyone, you've got problems. Check with your Server Administrator to ensure that your email script is secure and that email relays have been disabled on that email account.
If the sp@m is becoming a problem, institute a captcha image script to prevent bots from submitting the form. There are tons of free captcha scripts out there.
Here's a link to more info:
The Official CAPTCHA Site