Can a District Council (Urząd Dzielnicy) refuse to update/issue PESEL UKR number if 30 days have passed since the date of a person’s entry to Poland?

Yes. According to the Special Act (specustawa), the deadline for registering the stay of a Ukrainian citizens in Poland if the said Ukrainian citizen has not been registered by the commanding officer of the Border Guard post during border control is 30 days. 

In such a case the registration of their stay takes place upon request of the Ukrainian citizen, in which case the application for the registration of stay is the for the issuance of a PESEL number. Hence the rule that the application for issuing a PESEL number (which is equal to the application for the registration of stay of a Ukrainian citizen by the Commander-in- Chief of the Border Guard) can be submitted by the foreigner within 30 days from the day of entry into the territory of the Republic of Poland.

However, if the question is not the issuance of a PESEL number but rather updating a PESEL number to a PESEL UKR number, applicants should inform the respective District Council that pursuant to article 4 section 2 of the Special Act, the 30-day period concerns submitting the application referred to in article 4 section 1 of the Special Act, i.e. the application for assigning a PESEL number, whereas the possibility of granting the status of PESEL UKR to a person whose PESEL number was assigned before the entry into force of the Special Act is regulated in article 4 section 1a of the Special Act, which is not subject to any time limit.