Look at decorative parts during ordinary cleaning, paying particular attention to edges, seams, attachment points and areas your cat bites or scratches. Gently check for unexpected movement without pulling harder than normal use would require.
Loose fabric, exposed filling, cracked supports or detached pieces should be assessed before the cat continues using that area. A decorative cover may conceal a structural component, so compare what you see with the assembly diagram rather than assuming all petals or leaves are cosmetic. Photograph damage clearly and contact the supplier with the model details. Avoid covering a problem with tape, staples or an improvised repair that creates new accessible edges. If you cannot isolate the damaged part safely, remove access to the whole item until you have suitable advice or the correct replacement component.
Use a torch to view a dark underside or seam while the cat is elsewhere. Comparing it with an earlier photograph can help distinguish a new gap from an intentional construction detail without pulling the part apart.
For product comparisons alongside this advice, see Linden wooden cat tower and Arbor Retreat. The details below explain their sizes and uses.
Further reading: cats.org.uk.
Linden wooden cat tower
Arbor Retreat
Floral Canopy