Certainly true Christians can backslide, if by that you mean they can regress into a period of spiritual dullness or disobedience. Those who do so will bring God's discipline (Hebrews 12:6-11). That's because God disciplines those who are true sons (v. 8).
But no, if you are thinking of backsliding as a perpetual state of willful rebellion or ungodly indifference on the part of one who professes faith in Christ. That situation is a sign of false profession (Matthew 7:21-23; 1 John 3:4-10).
The word backsliding is used two ways in Scripture. It is found only in Old Testament references to the nation of Israel (Jeremiah 3:22; 31:22; 49:4; Hosea 4:16; 11:7; 14:4, KJV).
- Sometimes it speaks of backsliding as the action of unregenerate people who turn stubbornly away from God (cf. Jeremiah 8:5). In that sense the Word cannot be used to describe true Christians.
- Other times true believers are said to backslide (Jeremiah 14:7). All believers go through times when they do not grow or are set back in their growth by sin--they seem to be sliding backwards like a calf on a muddy slope (cf. Hosea 4:16, KJV). In that sense the word could apply to true believers.