No. Infringement affects businesses of all sizes, and small businesses are often targeted precisely because the perpetrator assumes the owner lacks the resources to respond. A brand that has built customer recognition is worth protecting regardless of the company's size.
The scope and cost of monitoring can be calibrated to the budget. A small business may choose to monitor only the most relevant trademark registers in its primary markets, rather than running full multi-channel global surveillance. Even a basic monthly search of the relevant IP office database is better than no monitoring at all.