This seems to be borne out by it seemingly being the same clubs getting relegated and promoted over the years.
not really
05/06 - Sunderland and Birmingham back at first time, West Brom back a year later
06/07 - charlton and Sheffield united not back and now in league 1, Watford back after 8 seasons with new owners
07/08 - Derby not back, Birmingham promoted the following season and reading 4 seasons later
08/09 - Newcastle and West Brom back immediately, Middlesbrough back after 7 seasons
09/10 - hull back after 3 seasons, Burnley after 4, Portsmouth never returned in league 2 for a while
10/11 - West Ham back the following season, Birmingham not back, Blackpool in league 2
11/12 - Blackburn not back, wolves not back and went to league 1 and Bolton now in league 1
12/13 - qpr promoted the following season, Reading not back, Wigan dropped to league 1
13/14 - Fulham and Cardiff not back, Norwich promoted the following year
14/15 - hull and Burnley back at the first attempt, qpr not back
in the last 6 seasons (where they have had a chance to come back up):
- Blackpool and Portsmouth now in league 2
- Wigan, Bolton and wolves have spent time in league 1
- 5 out of 18 have come back at the first attempt
- 7 of the 18 returned at some point (Burnley and hull twice, Norwich, qpr, West Ham)
- 6 out of the 18 have been stuck in the championship
Odds are less than 1/3 to come back up immediately and just over 1/3 to come back up eventually, stretch that out over the last decade it's 1/3 that come up at the first time of asking (interesting only 1 has come up the second season after, probably as that's when the big cost cutting happens for the majority as they become championship clubs). 7/30 teams had a further relegation, some of these are probably down to poor management (Pompey, wolves, Wigan, charlton spring to mind here getting relegated again within 2 years of leaving the prem)