Packet loss between differents clients and the gateway

[Marcelo Menchi]

Every day we have differents clients that loss packets with our Router Cisco 3800, the clients are in differents switches in our LAN and not always were the same clients how loss the connectivity with the gateway. 

We tried to connect a PC with that problem in the same switch that is the router but the problem persist, the router's logs didn't show anything and the switches neither. 

When a client loss packets with the router the client could ping any other client o switch on the LAN without problems (see picture above).

I need to find the problem. Thanks! 

[Mark Malone]

whats does the cpu history look like on the 3800 , show proc cpu his , is it stable or maxing out ?
if client can still ping everything on local the router still working and processing the packets for that subnet , when your on the router itself and the issue is occurring can you ping the gateway Ip locally from cli not the client ?
Theres no acl on the interface your trying to ping or coming from or restricted software firewall rules
Is it intermittent or constantly like this

[Marcelo Menchi]

The CPU of the router is stable. 

The router is the gateway and when the issue is ocurring if a ping the client with problems from the router I loss packets too, but I can ping another clients without problems. 

There isn't acl and any other restriction, in fact, all was Ok one month ago, from this moment to now only we add 3 news switches to our LAN but there are not hops between the client and the gateway.