Whilst MAG may not be the best at marketing the airport, if the demand for seats to/ from BOH was there the airport could virtually sell itself. Going all the way back to 1965 when SOU's concrete runway opened, all the airlines moved out. Many have tried since, Dan Air, Euro Direct, Air Berlin etc, all have been and gone. Maybe BOH isn't in the right place to attract enough traffic to purely rely on passenger throughput?
Getting to and from SOU is so easy by public transport while BOH is a complete nightmare. SOU quote 99 steps to its railway station and has a great bus service. BOH has a single bus service with a gap of up to 3 hours during the day between services. The last bus of the day runs at 18:30!!! This is something that MAG can't fix unless they pay for a better service and because they can't fix it BOH will always suffer.
The truth is for most of the day passengers standing on the platform at Bournemouth station can get to Southampton Airport far quicker by public transport than they can to the towns own airport and that is the problem in a nutshell as not everyone is willing to pay for a taxi.