Will reusing one condom cause pregnancy?

Not recommended. Depends on what you means by reusing. It is suggested that a fresh condom be used for every act of intercourse to avoid spillage. In general it would be difficult to reuse a condom. Therefore, pregnancy is a possiblity.
It can. Condoms are designed for single use only. Once used, they are stretched and are not as strong. Also, if used, there is semen in the condom which may enter the vagina. Always use a fresh condom, apply it correctly, and remove it quickly to prevent spillage or breaking.