Why the H+ ion remains with the molecule even though there is no bond between it and hyperconjugative structure?
Resonance structures do not exist on their own! Resonance is not a rapid equilibrium between different structures. It is a description of a single delocalised structure using contributing forms which only involve 2-centre-2-electron bonds. It is therefore meaningless to think about what would happen to an atom in a resonance contributor if it were left around.

In your example the two structures are resonance contributors to the single delocalised structure and so the hydrogen ion cannot move away from the molecule because it never exists on its own as a hydrogen ion. It is always bonded to the rest of the molecule.

Hyperconjugation can be explained through resonance but it is much more clearly explained through molecular orbital theory. In this picture you have donation of electron density from the $\ce{C-H~\sigma}$ orbitals into the empty $p$ orbital of the positively charged carbon. This is possible because the two orbitals can be aligned in a plane due to rotation around the C-C bonds.