Psalms 71:6
By thee have I been holden up from the womb: thou art he that took me out of my mother’s bowels: my praise shall be continually of thee. By thee have I been holden up from the womb: thou art he that took me out of my mother’s bowels: my praise shall be continually of thee.
God has held the speaker up from the womb, sustaining him from birth and from the very beginning of life onward. That lifelong upholding makes Him the source of the speaker's trust and the reason praise belongs to Him continually, as ongoing praise rooted in lifelong dependence. In mortal illness while facing death, Hezekiah could therefore appeal to God as the One who had upheld him throughout his life, pleading this lifelong trust and asking God not to forsake him as his strength failed.
He wanted to live on so that he could proclaim God's power to future generations. The continual praise is praise that keeps going without stopping, to be spoken out openly rather than kept secret, like the healed woman who was asked to acknowledge her blessing.
Every person is to confess God's faithfulness from distinct personal life and experience of divine power at work within, and God wants that praise to carry each person's own individuality. Such acknowledgment of grace, when supported by a Christlike life, is Heaven's chosen way to reveal Christ to the world. It has irresistible power working for the salvation of souls.