Budget constraints can lead to Facebook ads not delivering for a few reasons:

Insufficient budget: If the budget allocated for the Facebook ad campaign is too low, the ad may not have enough resources to reach its intended audience. Facebook's algorithms prioritize ads with higher budgets, so a low budget may result in the ad not being shown to as many people.

High competition: If the ad is targeting a highly competitive market or a popular keyword, it may require a higher budget in order to compete with other ads for the same audience. If the budget is not sufficient, the ad may not be shown as often.

Narrow targeting: If the ad is targeting a very specific or small audience, it may require a higher budget in order to reach that audience. A low budget may not be enough to reach the intended audience, resulting in the ad not delivering as expected.

To overcome budget constraints and ensure that the Facebook ad is delivering effectively, it may be necessary to increase the budget or broaden the targeting to a larger audience. It may also be helpful to review the ad's targeting and optimize it to reach a more relevant audience.

Read up on other issues as to why your Facebook Ads may not be delivering:
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1. Ad Quality: Facebook's algorithm is designed to show the best ads to its users, so if your ad isn't delivering, it could be because it's not up to par. Make sure your ad is visually appealing, has a clear call to action, and is relevant to your target audience.
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2. Ad Frequency: If your ad is being shown too often, it could be causing users to tune it out. Try decreasing the frequency of your ad to see if that helps.
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3. Placement issues: Another reason your ad might not be delivering is if it's being placed on low-quality websites or in low-quality placements. Make sure you're targeting the right placements for your ad and consider excluding placements that don't perform well.
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4. Ad relevance: Facebook's algorithm is designed to show ads that are relevant to users, so if your ad isn't delivering, it could be because it's not relevant to your target audience. Make sure your ad copy and imagery are relevant to your target audience and try A/B testing different ad variations to see what works best.

Curious how targeting issues can hinder your Facebook Ads? Check out this piece.