Additionally, it may be noted that PuLP is not the Binary LP solver, but the default solver within the PuLP framework is CBC. So it is CBC that is failing to get you the solution. In case you don't mind sharing your problem, you may share your LP file and it can be tried using other solvers, like, Gurobi, Cplex or some nice tricks that I can try out on your behalf!
In case you don't know, after you define the problem in PuLP (say, the model is called prob), you can save the .lp file as:
prob.writeLP("YourProblem.lp")
Best regards,
Sam