One of the problems we face, is we have no good definition of time that can equate time to energy and matter so we can know proportional relationship. Time tends to remain a philosophy variable resulting in philosophical science. It is stuck as a reference variable, in a world where reference is relative. This allows anything you wish from time. What we need is a tangible link to known science that is not based on philosophical reference.
The closest tangible science concept to time, in terms of functionality, is entropy. Both entropy and time, within the universe, move in one direction; time moves forward and entropy will increase. Energy/mass is conserved and therefore stays the same so it does not flow like time.
Since entropy needs energy to increase, you cannot get infinite entropy out of a finite amount of mass/energy. The amount of theoretical entropy is proportional to the amount of mass/energy. This suggests that time cannot be infinite with a finite amount of mass/energy.
As entropy increase in one direction and time flows forward, mass/energy is absorbed into entropy, causing the usable mass/energy of the universe to decrease. The energy is conserved, but no longer useable once it is converted into entropy, since the entropy of the universe cannot decrease nor can universal time be made to go backwards.
Entropy, by decreasing the useable mass/energy, places mass/energy into the stream of time; useable mass/energy of the universe decreases with time. As time moves forward, useable mass/energy is lost. We will have only a finite time until entropy maxes out, by absorbing all the useable mass/energy. Without useable energy, there are no further changes of state possible. Since time is defined as changes of state, time will stop.