To find programmes that are available for longer than 7 days you will need to use the 'Search' function.BBC iPlayer FAQ said:How long are programmes available for on BBC iPlayer?
In general, programmes are available for up to seven days after their original broadcast. However some programmes may only be available for shorter periods.
If a programme is repeated during these seven days on one of the main BBC TV channels or radio stations, we normally extend the programme availability. For some TV series, each episode is available for up to seven days after the last episode has been broadcast, as part of Series Catch-Up. We're also currently trialling this for radio. If we offer downloads, you can download previous episodes to BBC iPlayer Downloads, but only the most recent episode will have a 'More downloads' option.
In addition, some series offer programmes beyond seven days on their websites.
BBC iPlayer Downloads
Most TV programmes are available to download from the BBC iPlayer site and are available for seven days. Once downloaded, you have up to 30 days to play the programme, and once played you have up to seven days to finish watching the programme.