Sony Europe’s Decommissioned Servers page was updated recently and confirmed the end of online play for a pair of first-party kart racers. The original ModNation Racers on PlayStation 3 and its DLC have already been delisted from sale in North America and Europe but its online features will hold out a little longer. Unfortunately, there are conflicting dates at the moment with PlayStation.com (North America) indicating July 10th as the last day to play online while Sony Europe is now saying October 10th. These may be regional differences but if you plan to play, do it before July just in case.
Multi-player and all online features for this product will be terminated and will no longer be available on 07/02/2018. You will still be able to create content but will not be able to share it with other LBPK players.
Online play for LittleBigPlanet Karting has received the same fate — the plug will be pulled on July 2nd, worldwide — but the game has yet to be removed from sale on the PlayStation Store. Fortunately, being first-party titles, both games are readily available on physical media (ModNation, LBP Karting) and if you hurry, GameStop still has download codes for the games and a lot of their DLC (ModNation, LBP Karting).