In my experience of being in the social housing bid system a few times, I would say if you're repeatedly coming up in the top five or six bidders, then hang on in there, don't change your situation as you should have a successful bid sometime soon.
Obviously it depends how many properties are coming up on the bid system per week. If for example you're eligible for a 2 bed flat and there's a steady supply of 2 bed flats coming up every week, then you're in good stead over time.
One of the problems with the bid system is that the council will always give priority to people who have agreed to 'downsize'. Also in my personal opinion, allocations officers or housing staff can be a bit shady and there may be stuff goes on that isn't quite how it should be.
Make sure to learn how the system works. If you're in the top 10 bids when the bidding closes, email or phone every single time to ask if you'll be invited to the viewing. If you attend the viewing make sure to be informed of who the successful candidate was and assured that the flat has been allocated. Sometimes the number one, or two, or even three, bidder drops out or declines.
Doesn't matter if you feel like you're pestering them, let them know you are desperate, you're keeping an eye on the bid system and the allocations. If you haven't got anywhere over time, keep a record of your high bids but the fact you've not been offered anything and maybe go see a local councillor or MP.
Also, if you haven't already, scrutinise the allocations policy and the points / banding / priority awards (it's always published on their website) and if necessary go to a local legal advice centre to check there's not any points that you're missing - the council in my area never give people their full points or priority without a lot of pressing from advocates. When they realise you know their system, they stop playing stupid games.
Also, check online to see if there's any Housing Co-operatives, or Housing Associations you could be eligible for that aren't via the council bid system.
If you take private rented at this juncture, you'll be stuck in private rented for years to come. Stick it out if you can bear it and good luck.