Can a creature block if it was given summoning sickness after being declared as a blocker?

Summoning sickness (the rule that prevents a creature from attacking or activating tap/untap abilities) is checked only at the moment a creature is declared as an attacker or blocker. It is not an ongoing condition that continuously re-evaluates whether a creature can remain in combat. This is governed by CR 302.6, which restricts attacking and using certain activated abilities, and CR 509.1, which defines when blocker legality is checked.

Once the declare blockers step is complete and a creature has been legally declared as a blocker, it is now in combat as a blocking creature. If it somehow gains summoning sickness after that point — for example, due to a card effect that gives it a 'summoning sickness' style restriction — that does not retroactively make its declaration illegal, nor does it remove the creature from combat (CR 506.4 covers how creatures leave combat).

It is worth noting that summoning sickness itself only applies at the start of a turn; a creature does not naturally 'gain' summoning sickness mid-game in normal gameplay. However, some cards create copy effects or similar that might impose such restrictions. In any case, the key point is that blocker legality is a snapshot check at declaration time, not a continuous one.

Example: Your Grizzly Bears legally blocks an attacking creature during the declare blockers step. Your opponent then plays a spell that gives Grizzly Bears a 'cannot attack or block' equivalent effect. Grizzly Bears is already a declared blocker and remains in combat, dealing and receiving damage normally in the combat damage step — the after-the-fact restriction does not pull it out of combat.

Note: If a card explicitly says 'remove that creature from combat,' that is a different effect and would work regardless. But summoning sickness alone, gained after declaration, has no such removal effect (CR 302.6, 509.1b, 506.4).