The accrual almost certainly continued during the deferral period, but the exact answer lives in your specific PPM language, and I would not act on a general rule when real money is on the table.
Here is what those terms usually mean. A preferred return is the minimum annual return you get before the sponsor earns their share of profits, often something like 8% per year. Cumulative means any shortfall from a period you did not get paid carries forward and has to be made up before the sponsor takes anything. The word cumulative is what matters most here: it implies the clock kept running.
A deferral in most structures means the sponsor delayed paying you, not that they paused your economic entitlement. So if your 8% preferred return on $25,000 works out to $2,000 a year, and you received nothing for six months, a cumulative structure typically means you are owed that $1,000 before they collect a dollar of promote (the sponsor's profit share above the preferred return).
The ambiguity you are describing, whether accrual continued or restarts, is a genuine drafting gap that some PPMs handle poorly. The difference over 18 months on $25,000 at a typical preferred return rate could easily be $2,500 to $3,500 in your favor, so this is worth resolving formally, not informally.
I would do two things. First, ask the sponsor in writing to confirm their interpretation and the specific section they are relying on. Second, have a real estate attorney review the PPM language before you accept any calculation they send you. That is squarely legal territory and a professional needs to read your actual document.
What does the PPM say about how the preferred return accrues, specifically around distribution suspension or deferral? That clause, if it exists, is usually where the answer is hiding.