How to implement a node limit per taxonomy term?
You can make this work by using Rules in combination with the Views Bulk Operations module, as further detailed in the "blueprint" below.

Step 1

Use the Views and Views Bulk Operations module to create a view of all nodes that have a specific taxonomy term, in which you add a VBO field to it. Simply include a field like nid for each node (no need for any other fields). Just make sure you get exactly 1 row for each node you want to take into consideration.

Step 2

Create a Rules Component like so:


Using these Rules Component parameters:


a parameter of data type that matches with the data type of your 'Taxonomy with "limit" field' (probably "integer"), let's assume the parameter has machine name node_limit.
a parameter that matches with the term reference field as defined in your node's content type, let's assume the parameter has machine name node_termreference (which can be either a single value, or it can have multiple values, depending on how you defined it in your content type).

With a Rules Condition "Check number of results returned by a VBO view", whereas:


you select the VBO view created in Step 1.
you want to check if that number of results is greater or equal to  node_limit (which is the 1st parameter used by this Rules Component).

Rules Actions:


Set an appropriate Drupal message (that the node limit for that term has been reached already).
Remove the term that was entered from the node_termreference field (which is the 2nd parameter used by this Rules Component); Which Rules Action to use for doing so depends on how that field is defined, e.g if it is a multi value field, then you should use "remove from list".



Step 3

Create a custom Rule like so:


Rules Events:


Before saving a new node (optionally limited to relevant content types).
Before updating an existing node (optionally limited to relevant content types).

Rules Conditions:


Entity has field, for the field that refers to your taxonomy term (to make this field available for further processing in your subsequent Rules conditions/actions). More specifically we'll need it (as a token) to specify a value for the node_termreference parameter to execute the Rules Component from Step 2 later on.

Rules Actions:


Fetch entity by ID, whereas you fetch the taxonomy term entered in the node being created or updated. By doing so, your 'Taxonomy with "limit" field' will become available as a token in subsequent Rules Actions. More specifically we'll need it (as a token) to specify a value for the node_limit parameter to execute the Rules Component from Step 2 later on.
Execute the Rules Component from Step 2, by passing that Rules Component the appropriate values for node_limit and node_termreference to actually perform its logic.



Done! .... only using (popular) contributed modules, with no custom code involved .... All you need is Rules, Views and Views Bulk Operations.

PS: the above is only a blueprint ... Mostly because your question has not sufficient details. E.g you didn't explain how those terms are defined in your content type).