The nature of eternal life is not a reference to the duration of the life, but the quality and source of the life, Jesus Christ(a). Many verses which describe how to obtain eternal life (ie. John 3:16) are conditional upon a continual belief. This idea can be lost in our English translation (b).

a. John 3:16 "For God so loved the world that He gave His only begotten Son, that whoever believes in Him should not perish but have everlasting life."

"believes" (present tense/active voice)
"should not perish" (aorist tense/middle voice/subjunctive mood)
"have" (present tense/subjunctive mood)

Translation of the text taking the Greek tenses into account:

John 3:16 "For God so loved the world that He gave His only begotten Son, in order that each (one) who is himself continuing to believe in Him should not cause himself to perish, but may keep on having everlasting life."

John 10:27-28
27 "My sheep hear my voice, and I know them, and they follow Me.
28 "And I give them eternal life, and they shall never perish; neither shall anyone snatch them out of My hand.
(NKJV)

We have a similar situation in this passage as in John 3:16. The verbs are in the present tense, indicating a continuous action. That is, "My sheep are hearing My voice, and I know them, and they are following Me. And I am giving to them eternal life, and they shall never perish; neither shall anyone snatch them out of My hand." Jesus continually gives His "everlasting life" to His sheep who are hearing His voice and following Him. This passage does NOT imply that Jesus gave everlasting life to His sheep who heard His voice and followed Him. As in John 3:16, there is a continuous reciprocal action going on here. We have the same kind of activity described by John in His first Epistle, again using present tense verbs. "But if we are walking in the light as He is in the light, we continue having fellowship with one another, and the blood of Jesus Christ His Son is cleansing us from all sin." (1 John 1:7)

b. John 17:3
3 And this is life eternal, that they might know thee the only true God, and Jesus Christ, whom thou hast sent. (KJV)

Notice, Jesus did not say that you get eternal life by knowing Him. He said eternal life IS knowing Him. Eternal life is NOT something apart from God Himself. Having "eternal life" is having Christ in us, and us in Him. He is eternal, and He is life! The life that flows from Him cannot be exhausted.

John 1:4
4 In Him was life; and the life was the light of men.

Jesus is Life! He lives in us through His Spirit, and we live "in Him." Eternal life is not something apart from God Himself. He has infused Himself into us. His own life flows in and through us because we are "in Christ." Paul did not originate the idea of being "in Christ," Jesus did. Paul simply borrowed it.