One way would be to create the variable line once before the loop, and update its YData inside the loop.
% some random rh:
rh = 100*rand(1000,4);
assex=[0 25 25 30.7];
figure(1)
set(gcf, 'Position', get(0, 'Screensize'));
ylim([0 100]); yticks(0:2.50:100)
xticks(-1:1:35); xlim([-1 35])
xlabel('Spessore provino (cm)','FontSize',18)
ylabel('Umidità relativa aria (%)','FontSize',18)
set(gca,'FontSize',15)
grid on
xline(assex(1),'k',{'Superficie interna'});
xline(assex(2),'k',{'Freno a vapore - lato interno'},'LabelHorizontalAlignment','left');
xline(assex(3),'k',{'Freno a vapore - lato esterno'});
xline(assex(4),'k',{'Superficie esterna'});
% create the line once:
my_line = line('XData',assex,'LineStyle','-','Color',[0 0.4470 0.7410]);
for k=1:60:size(rh,1)
% set the line's YData each time:
set(my_line,'YData',rh(k,:))
title(string(strcat('Tempo= ',num2str(k/60,'%.2f'),' ore (',num2str(k/(60*24),'%.2f'),') giorni.')))
drawnow
end
