Remember that relationship with Christ is like any relationship, especially marriage. You won't always feel vibrant and worshipful. There are times you may feel as though you've wronged or offended Him, and times you may feel hard of heart. These are times to seek repentence and reconciliation with the Lord.
Being alive, depending on what the person asking you meant by it, could mean that feeling of being 'in love' where you're emotionally very close to God. It could also mean keeping to the Word that is written in your heart - doesn't guarantee you don't sin, but it makes you more cognizant of it and especially of your life as a whole. If you like, call being alive the awareness of the Grace that abides in you and allows you to follow Him in the first place.