Short answer. Your appeal risks dismissal. Rule 44 provides that the failure of the appellant to file his memorandum within the non-extendible thirty-day period may be a ground for dismissal of the appeal — it is not automatic, but missing that deadline exposes your case to that consequence.
What the law says
The failure of the appellant to file his memorandum within the period therefor may be a ground for dismissal of the appeal.
Rule 44, Section 10 — Time for filing memoranda in special cases. Read the full provision →
The thirty-day, non-extendible deadline
Rule 44, Section 10 sets a firm window for these special proceedings: in certiorari, prohibition, mandamus, quo warranto and habeas corpus cases, the parties shall file, in lieu of briefs, their respective memoranda within a non-extendible period of thirty days from receipt of the notice issued by the clerk that all the evidence, oral and documentary, is already attached to the record. The thirty days run from that clerk's notice, and the rule labels the period non-extendible.
What missing that deadline can cost you
The consequence for missing it is stated directly: the failure of the appellant to file his memorandum within the period therefor may be a ground for dismissal of the appeal. Filing your memorandum late in one of these special proceedings puts your appeal at real risk of being dismissed on that basis alone, separate from whatever merit the underlying petition might otherwise have.
"May be a ground" is discretionary, not automatic
The article's own wording is worth reading carefully — it says the failure may be a ground for dismissal, not that dismissal automatically follows. That leaves the court with discretion over whether to dismiss the appeal for a late memorandum. But discretionary is not the same as unlikely, and nothing in the rule guarantees the court will excuse a missed deadline, so treating the thirty days as firm is the safer course.
Why a memorandum instead of a brief in these cases
This rule applies specifically to certiorari, prohibition, mandamus, quo warranto, and habeas corpus proceedings, where the parties file memoranda in lieu of briefs — a different track from an ordinary appeal's brief-filing schedule. Because the period is expressly made non-extendible, the usual routes for buying extra time that might apply to other filings are not available here, which is part of why the deadline is treated so strictly in this particular class of proceedings.
What to do if the deadline is close
Because the period runs from the clerk's notice that the record is complete rather than from the filing of the petition itself, it is worth tracking exactly when that notice was received rather than estimating from the petition's filing date. Given that the rule labels the period non-extendible and treats a late filing as a possible ground for dismissal, filing the memorandum as early as it can reasonably be prepared, rather than close to the thirtieth day, avoids leaving the outcome to the court's discretion.