I've rarely been in monogamous relationships and when I was...I always felt "trapped" after a few months.
Both my long term marriages have been open, and although I don't think this "strengthens" the relationship it definitely prevents you from blaming your partner for not getting enough sex when things have died down. Overall TRUST TRUST TRUST and honesty is the key to a successful relationship, not hot sex. THAT never really lasts......1000 times with the same person has a way of becoming boring no matter who you're sleeping with.