I’m sorry to hear that you are having trouble with your IL SNAP link. I understand how frustrating it can be to not receive your benefits on time. Here are some possible reasons and solutions for your issue:

According to the Illinois Department of Human Services (IDHS), the date you receive your benefits depends on the last digit of your Social Security Number (SSN). For example, if your SSN ends with 0, you will receive your benefits on the 1st of every month. If your SSN ends with 9, you will receive your benefits on the 10th of every month. If you have recently changed your SSN or applied for a new one, this may affect the date you receive your benefits.
You can check your Link account balance online at the Illinois Link Card Website or by calling the Illinois Link Help Line at 1-800-678-LINK (5465). You will need your 16-digit or 19-digit card number or your 4-digit PIN to access your account. You can also use these methods to report a lost or stolen Link card, order a replacement Link card, change your PIN, check recent purchases and withdrawals, and report a problem with a purchase or withdrawal.
If you have moved or changed your address, income, or assets, you need to report these changes to IDHS as soon as possible. You can do this online at Change My Address, Income or Assets for Cash, SNAP and/or Medical Customers or by contacting your local IDHS office. You can find the nearest office by using the Office Locator. Failure to report changes may result in delays or reductions in your benefits.
If you have questions about the eligibility criteria, application process, or benefit amount for SNAP, you can visit the How to Apply for Cash, SNAP & Medical Assistance page or call the IDHS Help Line at 1-800-843-6154. You can also use the SNAP Calculator to estimate how much SNAP benefits you may receive.
Here are some additional things you can do:

Try calling the IDHS Help Line again at a different time of day. The lines are usually busiest during the morning and early afternoon.
Try calling the Help Line from a different phone number. Sometimes, the automated system will block your call if you have called too many times in a short period of time.
Try using the IDHS online chat feature. You can find this on the IDHS website.
If you are still unable to get in touch with the IDHS, you can try visiting your local IDHS office. You can find the address and hours of operation for your local office on the IDHS website.
When you do get in touch with the IDHS, be sure to have the following information ready:

Your full name
Your Social Security number
Your date of birth
Your case number (if you have one)
The date you were approved for SNAP benefits
The date you were supposed to receive your IL SNAP link
The IDHS representative should be able to help you determine why you have not received your IL SNAP link and when you can expect to receive it.

I hope this helps!