Getting reinfected with H.Pylori is rare as a person usually gets immunity after their first infection. However one can get infection twice depending on the virulence of organism and immunity of patient. For more details visit http://www.helico.com/faq_infection.html#Q11
Yes, you can get an infection from this more than twice. Unlike some diseases, the body does not usually form long lasting antibodies against bacteria of this nature. That is why most people have reoccurring bacterial infections.