Assuming that the whole universe doesn't collapse upon itself, would matter eventually lose cohesion at an atomic level and cease to exist?
The ultimate fate of matters depends on whether protons decay.
Some theories of unification requires that protons decay. The decay mechanism is:
Proton decay has not yet been observed and the lower limit for its half life is
Neutrons, which are heavier than protons, have a half life in their free state of about 10 minutes. Neutrons decay into a proton and an electron. Bound neutrons have a half life in the order of that of protons.
So, if protons decay then ultimately all matter will decay.