I think that we're missing some details. Any Arduino will reset if you remove and re-apply the power.
- Which Arduino are you talking about?
- Which SMS module / shield are you using?
- By unplugging, do you mean disconnect from the PC?
- How do you power the Arduino? Via USB? Or with and external power supply? If the latter, what exactly.
Your topic has been moved to a more suitable location on the forum. Installation and Troubleshooting is not for problems with (nor for advise on) your project
See About the Installation & Troubleshooting category.