does the Buyer have the right to not resume the relationship and not be liable for the balanced payment or at least not immediately?
There are a few gaps and inconsistencies in your description, which appears to relate to the linked post in regard to the purchased item (the pay-as-you-go service mentioned there is a separate contract that will be ignored here). Subject to missing details, (1) the buyer is not entitled to unilaterally terminate the [purchase] contract, and (2) the seller cannot force the buyer to make a lump-sum payment of a balance the they agreed would be paid in installments.
The statements that "[s]eller prematurely terminated the agreement" and thereafter "decided to abide by the initial terms" suggest that actually the agreement had not been terminated. The seller merely desisted from amending or replacing the original agreement. The seller might be --or might have been-- in breach of contract at some point, but that is different from terminating that agreement.
Nor does a party's breach necessarily entitle the counterparty to terminate that agreement. Generally speaking, that entitlement would have to be provided in the agreement. In some situations, a contract is voidable by a party. See Restatement (Second) of Contracts at §153. However, the scenario you and the other OP describe would not warrant that remedy.
The seller's alleged inability to reinstate its automated deductions does not release him from his duty to perform the deductions as scheduled in the agreement. Even if the seller's [questionable] allegation is truthful, nothing appears to prevent him from processing the deductions manually.
It is possible that manual processing of deductions translates to additional costs to the seller. To reduce those costs, the seller could devise lawful (i.e., not coercive, not misleading, etc.) incentives that would persuade the buyer to agree to a different arrangement. The buyer cannot be expected to waive a contractual right merely because the seller is adamant about the aforementioned inability.
The tables could turn if the customer terminates the relationship in a way that amounts to breach of contract. Based on the details provided so far, it is in the buyer's best interest to stick to the terms of the agreement unless [maybe] the seller comes up with a satisfactory proposal.