Nope! The deals are linked to your Burpple account and do not automatically refresh when you switch plans. The membership plan simply determines your access to your deals e.g. during off-peak hours for members on the Off-Peak plan and all day for members with All Day (Monthly or Annual) plans.
Each Beyond partner offers each member four deals that are redeemable before the stated expiry date. Partners have the option to renew their deals when they expire.