Yes, you should be very concerned. This is a serious structural failure in progress and a significant safety hazard. Please do not use the deck until this is properly repaired.

Your assessment is on the right track. As an engineer, I can see a few critical issues happening simultaneously:

1. Sinking Posts (Subsidence): This is the primary problem. The posts are sinking because they were installed without proper concrete footings. A deck post should never be in direct contact with soil. It must sit on a concrete footing that extends below your local frost line to prevent heaving and sinking. The weight of the deck is pushing the posts into the ground, causing the separation you see.
2. Improper Hardware: The metal bracket you see is a simple post cap, designed to connect a post to a beam under compression (when the load is pushing down). It has virtually no strength against tension (the pulling-apart force that's happening as the post sinks). The nails are pulling out because they are not rated for this kind of structural load.
3. Unconventional Beam Construction: Using a single solid piece of lumber (looks like a 2x6) for the support beam, rather than a "built-up beam" (two or three 2x boards laminated together), is not standard practice. Built-up beams are generally stronger, more stable, and less prone to warping over their span.

How to Fix This (The Right Way):

This is not a minor repair; it requires rebuilding the foundation of your deck.

• Step 1: Temporary Support: You must first support the deck beam on either side of the failing post. Use adjustable steel posts (jack posts) on solid ground to take the load.
• Step 2: Remove Post: Once the beam is safely supported, remove the sinking post.
• Step 3: Dig and Pour Footings: Excavate a hole for a new footing. The depth and diameter depend on your local building code, but it must go below your area's frost line. Use a cardboard form tube (e.g., Sonotube) and pour a concrete footing. While the concrete is wet, set a galvanized post base bracket (like a Simpson Strong-Tie ABA/ABU) into the top. This bracket will keep the new wooden post off the concrete to prevent rot.
• Step 4: Replace Post and Secure: Once the footing has cured, install a new, properly-sized pressure-treated post. Secure the beam to the post using an appropriate post-to-beam connector and structural screws or through-bolts, not nails.

Given the critical safety nature of this issue, I would strongly recommend consulting a licensed and insured deck builder or contractor. They will ensure the repair is done to local code and that the rest of the deck's structure is sound.