How do I track deadlines and penalties in a construction contract?

Short answer

Turn the contract dates into stages with start and end dates, not one single final deadline.
Track the client's payment deadlines separately — penalties run both ways.
Record every stoppage day and its cause in the site journal.
Notify in writing any cause of delay that isn't yours, at the moment it arises.
Calculate the penalty on actual days late, against the deadline as revised by addenda.

Civil Code, Art. 1538 — a penalty clause is one where the parties fix in advance what the debtor owes on non-performance; the daily late-delivery percentage in construction contracts is a penalty clause.
Law 72/2013 on combating late payment — between professionals the statutory penalty interest is the National Bank reference rate plus 8 percentage points, and the payment term may not, as a rule, exceed 60 calendar days.
Law 50/1991 on authorising construction works — the declared execution period and the permit's validity are deadlines distinct from the contractual ones, but they are tracked together.
The construction acceptance regulation (Government Decision 273/1994, as amended by Government Decision 343/2017) — the date of acceptance at completion is the point the warranty period starts running from.

Example: an 850,000 RON contract carries 0.05% per day late. At 18 days late the penalty is 7,650 RON. Of those 18 days, 7 are rain days recorded in the journal and notified to the client, so the discussion is about 11 days, i.e. 4,675 RON.
Example: the client is 40 days late paying a 120,000 RON work statement. With no contractual clause, statutory penalty interest is calculated at the reference rate plus 8 percentage points for those 40 days.

Tracking only the final deadline, so you learn about the slip when it can no longer be recovered.
Not notifying causes of delay outside your control in writing; when the penalty is computed, what was said verbally doesn't count.
Calculating the penalty against the original contract date, ignoring extensions granted by addenda.
Not tracking the client's payment deadlines, even though late-payment interest is something you can claim too.

Every stage has its own deadline, and the delay alert fires before the final deadline is missed.
Stoppage days and their causes stay dated in the daily journal, so the evidence exists when the penalty is discussed.
Stage progress is compared against the original plan, on every active site.
Progress reports sent to the client build a communication trail, useful when the deadline is renegotiated.