Manager isn't accessible via model instances

The error in question is caused when you try to access the Manager of a model through an instance of the model. You have used lower case class names. This makes it hard to say if the error is caused by an instance accessing the Manager or not. Since other scenarios that can cause this error are unknown I am proceeding on the assumption that you have somehow mixed up the topic variable so that you end up pointing to an instance of the topic model instead of the class.

This line is the culprit:

forum.topic_count = topic.objects.filter(forum = forum).count()
#                   ^^^^^

You have to use:

forum.topic_count = Topic.objects.filter(forum = forum).count()
#                   ^^^^^
#                   Model, not instance.

What is going wrong? objects is a Manager available at the class level, not to the instances. See the documentation for retrieving objects for details. Money quote:

Managers are accessible only via model classes, rather than from model instances, to enforce a separation between "table-level" operations and "record-level" operations.

(Emphasis added)

Update

See the comments from @Daniel below. It is a good idea (nay, you MUST :P) to use title case for class names. For instance Topic instead of topic. Your class names cause some confusion whether you are referring to an instance or a class. Since the Manager isn't accessible via <model> instances is very specific I am able to offer a solution.The error may not be so self evident always.

topic.__class__.objects.get(id=topic_id)

For django < 1.10

topic._default_manager.get(id=topic_id)

Though you should not use it like this. The _default_manager and _base_manager are private, so it's recomended to use them only if you're inside the Topic model, like when you want to use the Manager in a proprietary function let's say:

class Topic(Model):
.
.
.
    def related(self)
        "Returns the topics with similar starting names"
        return self._default_manager.filter(name__startswith=self.name)

topic.related() #topic 'Milan wins' is related to:
# ['Milan wins','Milan wins championship', 'Milan wins by one goal', ...]