Part of the problem is visitors who bring infections in - by coming to visit when they have a cold, or have been feeling a bit unwell but 'struggle on', by not washing their hands after a visit to the bathroom, by sneezing without turning their heads away or using tissues, by over using anti-bacterial sprays and cleaners at home, by not following good hygeine instructions posted in hospital wards; I could go on, but studies many years ago showed that the biggest culprits were hospital pens/keyboards and married hospital staff. Pens can travel the whole length of a hospital and keyboards are usually multi-user. Married hospital staff carried more germs on their hands than unmarried hospital staff - because very few of them removed their wedding rings to wash under them.
Contact with germs is inevitable and we mostly have a good immune system to counteract them but sometimes, the germ wins.
There is an episode of Scrubs which shows just how easy it is to pass on germs to an immuno-supressed patient from a sneeze in a corridor at one end of the hospital, to the patient's room at the other... it's very graphic and should be mandatory viewing for all who set foot in a hospital, regardless of their reason for being there.
Persistent infections can be counteracted by washing frequently with good old soap and water, being sensible with food preparation areas and equipment, using paper tissues and disposing of them carefully and sensibly, occasional disinfecting of things like musical instruments and telephones, having a fresh air intake into the house and not overheating it; all these things can help break the chain of infection and re-infection. If you keep getting colds, treat the cause, not the symptoms.