Is my work as a network technician in a company that provides continuous internet services and SMS services for religious channels and organizes competitions therein impermissible, knowing that my work is limited to maintenance and repair?

The fundamental principle is that there is no harm in providing internet or SMS services unless it is known that they are used for disobedience (to God), nor is there any harm in organizing competitions and selecting winners from them, unless they involve a Shariah-forbidden element. Your work as a network and media equipment technician, and the services provided by your company, are not inherently forbidden. Therefore, there is no harm in you continuing this work. Even if some prohibited matters are involved in your company's services, there is no harm to you as long as you have no connection to those specific services.