Which BOINC version you run (See Help->About BOINC in BOINC Manager). We'd just like the version number, please: for instance v7.8.2
There is no "Help / About BOINC" in the BOINC Manager menu.
The version listed under "Help / About BOINC Manager" is Version: 7.16.11 (x64) and wxWidgets Version: 3.0.1

What your problem is exactly, write it out in as much detail as you can.
It's not downloading any new tasks to process.
It had been running four tasks in calculation and listing four pending tasks. When it finished one, it started one of the pending tasks. When it transferred completed tasks out, it also transferred the same number of new tasks in
About 2 weeks ago, I noticed that it had downloaded more than the number of replacement tasks. The number of Pending Tasks had increased to 5. That seemed odd, but did not seem a problem.
About 6-7 days ago, the number of pending tasks dropped back to four, then over the next 2-3 days dropped to 3, then 2, then 1. It did not do this on consecutive downloads. It ran on each number for 2-3 downloads before dropping again. It now has no pending tasks and has completed and sent out all the tasks it had downloaded. The log now shows the following sequence of events, repeating at intervals of 10-60 minutes.

Checking presence of 4 project files
Suspending GPU computation - computer is in use
Rosetta@home | Sending scheduler request: To fetch work.
Rosetta@home | Requesting new tasks for CPU
Rosetta@home | Scheduler request completed: got 0 new tasks
Rosetta@home | No tasks sent

What you have done so far to try to remedy the problem.
Verified that the project is not suspended in any of the ways I can find to suspend or unsuspend it. Exited and restarted BOINC Manager. Rebooted the computer.

If applicable, the project(s) that you have the problems with and if they have multiple applications, which ones give you problems.
I am running only Rosetta@Home. I don't know how to tell whether it has multiple applications or not.

Post the first 40 - 100 lines from your BOINC Event Log (CTRL+SHIFT+E), including it showing what your BOINC is doing, which project tasks it is running.

8/6/2021 11:40:50 AM | | cc_config.xml not found - using defaults
8/6/2021 11:40:50 AM | | Starting BOINC client version 7.16.11 for windows_x86_64
8/6/2021 11:40:50 AM | | log flags: file_xfer, sched_ops, task
8/6/2021 11:40:50 AM | | Libraries: libcurl/7.47.1 OpenSSL/1.0.2s zlib/1.2.8
8/6/2021 11:40:50 AM | | Data directory: C:\ProgramData\BOINC
8/6/2021 11:40:50 AM | | Running under account owner
8/6/2021 11:40:50 AM | | OpenCL: Intel GPU 0: Intel(R) HD Graphics 620 (driver version 23.20.16.4973, device version OpenCL 2.1 NEO, 2404MB, 2404MB available, 184 GFLOPS peak)
8/6/2021 11:40:50 AM | | OpenCL CPU: Intel(R) Core(TM) i3-7100U CPU @ 2.40GHz (OpenCL driver vendor: Intel(R) Corporation, driver version 7.6.0.611, device version OpenCL 2.1 (Build 611))
8/6/2021 11:40:50 AM | | Windows processor group 0: 4 processors
8/6/2021 11:40:50 AM | | Host name: DESKTOP-C76CEKN
8/6/2021 11:40:50 AM | | Processor: 4 GenuineIntel Intel(R) Core(TM) i3-7100U CPU @ 2.40GHz [Family 6 Model 142 Stepping 9]
8/6/2021 11:40:50 AM | | Processor features: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pat pse36 clflush dts acpi mmx fxsr sse sse2 ss htt tm pni ssse3 fma cx16 sse4_1 sse4_2 movebe popcnt aes f16c rdrandsyscall nx lm avx avx2 vmx tm2 pbe fsgsbase bmi1 smep bmi2
8/6/2021 11:40:50 AM | | OS: Microsoft Windows 10: Core x64 Edition, (10.00.19043.00)
8/6/2021 11:40:50 AM | | Memory: 5.87 GB physical, 11.12 GB virtual
8/6/2021 11:40:50 AM | | Disk: 460.39 GB total, 361.93 GB free
8/6/2021 11:40:50 AM | | Local time is UTC -4 hours
8/6/2021 11:40:50 AM | | No WSL found.
8/6/2021 11:40:50 AM | | VirtualBox version: 6.1.12
8/6/2021 11:40:55 AM | | No general preferences found - using defaults
8/6/2021 11:40:55 AM | | Preferences:
8/6/2021 11:40:55 AM | | max memory usage when active: 3004.94 MB
8/6/2021 11:40:55 AM | | max memory usage when idle: 5408.89 MB
8/6/2021 11:40:55 AM | | max disk usage: 363.41 GB
8/6/2021 11:40:55 AM | | don't use GPU while active
8/6/2021 11:40:55 AM | | suspend work if non-BOINC CPU load exceeds 25%
8/6/2021 11:40:55 AM | | (to change preferences, visit a project web site or select Preferences in the Manager)
8/6/2021 11:40:55 AM | | Setting up project and slot directories
8/6/2021 11:40:55 AM | | Checking active tasks
8/6/2021 11:40:55 AM | Rosetta@home | URL https://boinc.bakerlab.org/rosetta/; Computer ID 6123465; resource share 100
8/6/2021 11:40:55 AM | | Setting up GUI RPC socket
8/6/2021 11:40:55 AM | | Checking presence of 4 project files
8/6/2021 11:40:55 AM | | Suspending GPU computation - computer is in use
8/6/2021 11:40:56 AM | Rosetta@home | Sending scheduler request: To fetch work.
8/6/2021 11:40:56 AM | Rosetta@home | Requesting new tasks for CPU
8/6/2021 11:40:57 AM | Rosetta@home | Scheduler request completed: got 0 new tasks
8/6/2021 11:40:57 AM | Rosetta@home | No tasks sent

In case the log doesn't show this, please give us:
• the CPU brand and model: Intel(R) Core(TM) i3-7100U CPU @ 2.40 GHz
• the GPU brand and model: I don't know where to find this
• the driver version(s) you have installed: driver for what?
• the operating system that you use: Windows 10 Home, v. 21H1, OS build 19043.1110

https://boinc.bakerlab.org/rosetta/server_status.php shows that at this moment the project has 1 task ready to send. So it's effectively out of work. Nothing wrong with your BOINC.