Then there must be Juniperus sabina somewhere in the vicinity.
The fungus causing pear rust is, like all rusts, a biotroph: it feeds on the living cells of the host plant over an extended period without killing it. It is not able to survive on dead plant material, so must either alternate with a different, perennial host, or produce resting spores to pass the dormant season. Pear rust alternates between pears and junipers.
On pears, the brown fungal growths produced on the underside of infected leaves release spores which cannot reinfect pear, but instead are wind-dispersed and infect several juniper species, causing perennial stem infections. In spring these produce orange, horn-like outgrowths, which in turn produce wind-blown spores that reinfect pears.
Having a perennial host, like juniper, enables the fungus to survive those periods when the alternate host is absent (if it is an annual) or dormant and leafless (as with pears) although this particular rust can also form perennial cankers on the bark of pear as well.
Removing all the infected leaves and burning them and finding a suitable fungicide seems to be the only way forward.
Hope you manage it Nothing nicer they tell me than a home grown fresh pear. (I am allergic to them so dare not eat one.).