An elderly man had pneumonia & was on abs with signs of improvement warranting cessation of abs. could a lingering infection exist without an acute decline in his condition over the next week? wbc same crp rising again. xrays unclear-pleural effusion

Yes it can: It is indeed possible for a chest infection to continue beyond the course of antibiotics especially if the antibiotic was not the correct choice to begin with. If his CRP is rising then it means ongoing inflammation. It is possible that he is developing pleuritis and a parapneumonic effusion. The best option would be to obtain sputum cultures to see if he warrants another cause of antibiotics