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Does the "Club of Helmets" have a fixed number as a limit?

I agree with @FearlessF :

don't think so

I also agree with @847badgerfan :

Pretty hard to get kicked out of that club.

Some of the Michigan fans have argued that the "Helmets" were permanently set as of the 1970's and can never change.  I strongly disagree with this.  Minnesota was a "helmet" in the early days of CFB up until WWII and they clearly are NOT now.  I think that the same thing can and will happen to teams that we think of as helmets today.  

That said, Badge has a good point.  Once you ARE a helmet, you don't fall out of that club for having a bad year or two or even necessarily for having a bad decade or two.  However, if you fail to "look like" a helmet for long enough, eventually you will no longer be a helmet.  Exactly how bad you have to be and for how long for this to happen are not explicitly stated but I strongly believe that the possibility exists.  

Another way to put it is that maintaining helmet status is considerably less demanding than attaining helmet status.  Consider, for example, if Wisconsin and Michigan met in this year's CFP Championship game: 

IMHO, the outcome of the game would be irrelevant to Michigan's "helmet status".  They already are a helmet and advancing to the CG is sufficient to remind everyone that they ARE a helmet.  Losing that game wouldn't hurt them at all and winning wouldn't really help because simply getting there would already have done more than enough to maintain Michigan's "helmet status".  

Conversely, the outcome of the game would be HIGHLY relevant to Wisconsin's "helmet status".  They aren't a helmet and winning NC's is a REALLY good way to become a helmet.  Getting to the CG is great but plenty of non-helmets have been to CG's.  Oregon made it in 2014.  Clemson wasn't a helmet yet when they first got there.  Auburn and VaTech both got to the BCSCG.  

Since PSU joined in 1993 (28 seasons from 1993-2020):

AP Appearances:

• 428 (91.8%) Ohio State, first nationally
• 351 (75.3%) Michigan, fourth nationally
• 288 (61.8%) Wisconsin, 12th nationally
• 282 (60.5%) Nebraska, 14th nationally
• 268 (57.5%) Penn State, 18th nationally
• 166 (35.6%) Michigan State, 27th nationally
• 153 (32.8%) Iowa, tied for 29th/30th nationally

It's tough to put a lot of stock in this, because some teams are overrated consistently, to start the season. Looking at #2 here.

That could be an influence for teams that consistently end up ranked lower at the end of the year than they started.

Which College Football Teams Are Always Overrated in August? | FiveThirtyEight

reseason darlings that fail to live up to hype
Teams that received votes* in either the preseason or final AP Top 25 Poll in at least 16 seasons, 1997-2016

[th][/th] [th]FINAL VS. PRESEASON RANK[/th]
[th]TEAM▲▼[/th] [th]AVG. PRESEASON RANK▲▼[/th] [th]SAME▲▼[/th] [th]BETTER▲▼[/th] [th]WORSE▲▼[/th]
Notre Dame	25.1	10%	20%	70%
Texas	13.4	10	20	70
Florida State	9.4	10	20	70
Penn State	25.2	5	25	70
Florida	12.0	0	30	70
Ohio State	8.0	5	30	65
Nebraska	19.1	0	35	65
LSU	12.2	0	35	65
Miami (Fla.)	17.7	15	25	60
Tennessee	15.9	15	25	60
Oklahoma	6.6	15	25	60
Michigan	15.0	10	30	60
Southern California	13.2	10	30	60
Virginia Tech	17.6	5	35	60
West Virginia	25.9	10	35	55
Texas A&M	25.2	10	35	55
Alabama	15.1	5	40	55
BYU	33.0	15	35	50
Georgia Tech	27.3	10	40	50
Georgia	13.8	5	45	50
South Carolina	26.9	20	35	45
Oklahoma State	26.3	20	35	45
Michigan State	22.7	20	35	45
Arkansas	31.1	10	45	45
Auburn	20.6	5	50	45
Wisconsin	19.1	0	55	45
Mississippi	29.2	20	40	40
TCU	22.2	20	40	40
Utah	30.5	5	55	40
Oregon	18.9	0	60	40
Boise State	25.3	15	50	35
Clemson	21.1	15	50	35

It is nice of Tennessee and Nebraska to provide us with a case study for exactly how long it will take for a 70s "Helmet" to lose their lofty status. 

They aren't there yet, as both could theoretically be "back" with the right hire. (As opposed to "wow, someone is actually winning at Minnesota? That's unheard of!")

That could be an influence for teams that consistently end up ranked lower at the end of the year than they started.
Which College Football Teams Are Always Overrated in August? | FiveThirtyEight
reseason darlings that fail to live up to hype
Teams that received votes* in either the preseason or final AP Top 25 Poll in at least 16 seasons, 1997-2016

I generally love 538's stuff but I'm REALLY not a fan of the way they did this comparison.  I think the more important question than how often a team under or over achieved relative to preseason ranking is "by how much"? 

My point is that tOSU's average preseason ranking for 1997-2016 was #8.  Their preseason and final ranking matched 5% of the time (once), did better 30% of the time (six times) and did worse 65% of the time (13 times).  That sounds bad but if they finished one place lower than they started 13 times and a whole bunch of places higher six times I'd argue that they were actually underrated on average.  It is a question of mean vs median. 

Looking at those years for Ohio State:

• Once in 20 years (5%) the Buckeyes finished where they started
• Four times in 20 years (20%) the Buckeyes finished within +/-1 of where they started
• Six times in 20 years (30%) the Buckeyes finished within +/-2 of where they started
• Nine times in 20 years (45%) the Buckeyes finished within +/-3 of where they started
• 10 times in 20 years (50%) the Buckeyes finished within +/-4 of where they started
• 11 times in 20 years (55%) the Buckeyes finished within +/-6 of where they started
• 12 times in 20 years (60%) the Buckeyes finished within +/-7 of where they started

Then they improved and regressed by double-digits twice each:

• Up 15 spots in 2012
• Up 12 spots in 2002
• Down 11 spots in 2004
• Down 10 spots in 2013

It is harder to figure out what to do with years when a team either starts or finishes unranked.  In the case of the Buckeyes it has been a while since they started unranked but they did finish unranked four times between 1997 and 2016:

• 1999 They started #9 then skidded to 6-6 and unranked
• 2000 They started #16 and finished 8-4 and barely unranked
• 2011 They started #18 then skidded to 6-7 and unranked
• 2001 They started #23 and finished 7-5 and not too far outside the rankings

crude or otherwise, I like it that ND and UT are #1 & 2