A potential PhD supervisor declined to accept me as a student; can I ask a second time?
You can always ask.

However, be prepared that the answer may easily be still "no". Direct funding is by no means the only resource that an advisor has to pour into a student. There is also the time investment of actually advising a student, assorted costs for overheads and utilities, as well as presumably some money to fund conference trips. This isn't even to speak of simple inter-personal matters, such as that the professor may feel that you are not a good fit for the lab culture.