Sixth-tier Poole Town and Hungerford Town have been told by the National League they do not have the required 500 covered seats across two stands.
"We argue it's a decision no reasonable tribunal could have come to," Poole chairman Chris Reeves said.
Both clubs have satisfied FA ground grading rules to stay in the division.
The National League said it would not comment on the specific details for both clubs, but told BBC Sport that "an independent panel will judge both appeals".
With two games remaining in the regular season, Poole occupy the last play-off place in fifth and Hungerford are two points behind them in sixth.
Should neither club be allowed into the play-offs, the next highest-placed eligible side would take their place.
Darlington have also been blocked from the equivalent National League North play-offs for the same reason and have also appealed against the ruling.
Poole and Hungerford are both in their first seasons in National League South, with Poole having been promoted three times in the past five years.
"National League South is the only step where, if you have the ground grading for the league in which you play and your efforts on the field justify promotion, you don't have until 31 March the following season to put things right," Reeves told BBC Radio Solent.
"Each year we have been promoted, we have satisfied the criteria."
Hungerford, whose rise through the non-league pyramid has been equally as fast as Poole's, are also unsure if they will be allowed to compete in the play-offs.
"It's very confusing what the league are asking everyone to do," manager Bobby Wilkinson told BBC Radio Berkshire.
"The league need to come out and clear up what exactly needs to be done. I feel for Poole, as they also don't know what's happening.
"It's not fun for the players not knowing our fate. We've all done what we need to do to stay in the league, so let us play and whoever makes the play-offs, makes them."
The FA said it would await the outcome of the appeals, which they expect before the end of the season, before issuing a statement.
Two National League South clubs face an uncertain wait for appeals against being barred from the division's promotion play-offs to be heard.